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<span>Work</span> </div> </a> <ul id="toc-Work-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Political_career" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Political_career"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Political career</span> </div> </a> <ul id="toc-Political_career-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Honors" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Honors"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Honors</span> </div> </a> <ul id="toc-Honors-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Works" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Works"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Works</span> </div> </a> <ul id="toc-Works-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Articles" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Articles"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Articles</span> </div> </a> <ul id="toc-Articles-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Émile Borel</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 50 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-50" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">50 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A5%D9%8A%D9%85%D9%8A%D9%84_%D8%A8%D9%88%D8%B1%D9%8A%D9%84" title="إيميل بوريل – Arabic" lang="ar" hreflang="ar" data-title="إيميل بوريل" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Emil_Borel" title="Emil Borel – Azerbaijani" lang="az" hreflang="az" data-title="Emil Borel" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A7%D9%85%DB%8C%D9%84_%D8%A8%D9%88%D8%B1%D9%84" title="امیل بورل – South Azerbaijani" lang="azb" hreflang="azb" data-title="امیل بورل" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%8F%E0%A6%AE%E0%A6%BF%E0%A6%B2_%E0%A6%AC%E0%A7%8B%E0%A6%B0%E0%A7%87%E0%A6%B2" title="এমিল বোরেল – Bangla" lang="bn" hreflang="bn" data-title="এমিল বোরেল" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – Minnan" lang="nan" hreflang="nan" data-title="Émile Borel" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%91%D0%BE%D1%80%D0%B5%D0%BB%D1%8C_%D0%AD%D0%BC%D0%B8%D0%BB%D1%8C" title="Борель Эмиль – Bashkir" lang="ba" hreflang="ba" data-title="Борель Эмиль" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%AD%D0%BC%D1%96%D0%BB%D1%8C_%D0%91%D0%B0%D1%80%D1%8D%D0%BB%D1%8C" title="Эміль Барэль – Belarusian" lang="be" hreflang="be" data-title="Эміль Барэль" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%95%D0%BC%D0%B8%D0%BB_%D0%91%D0%BE%D1%80%D0%B5%D0%BB" title="Емил Борел – Bulgarian" lang="bg" hreflang="bg" data-title="Емил Борел" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – Catalan" lang="ca" hreflang="ca" data-title="Émile Borel" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – Czech" lang="cs" hreflang="cs" data-title="Émile Borel" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – German" lang="de" hreflang="de" data-title="Émile Borel" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CE%BC%CE%AF%CE%BB_%CE%9C%CF%80%CE%BF%CF%81%CE%AD%CE%BB" title="Εμίλ Μπορέλ – Greek" lang="el" hreflang="el" data-title="Εμίλ Μπορέλ" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – Spanish" lang="es" hreflang="es" data-title="Émile Borel" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – Esperanto" lang="eo" hreflang="eo" data-title="Émile Borel" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – Basque" lang="eu" hreflang="eu" data-title="Émile Borel" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D9%85%DB%8C%D9%84_%D8%A8%D9%88%D8%B1%D9%84" title="امیل بورل – Persian" lang="fa" hreflang="fa" data-title="امیل بورل" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – French" lang="fr" hreflang="fr" data-title="Émile Borel" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – Galician" lang="gl" hreflang="gl" data-title="Émile Borel" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%97%90%EB%B0%80_%EB%B3%B4%EB%A0%90" title="에밀 보렐 – Korean" lang="ko" hreflang="ko" data-title="에밀 보렐" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%8F%E0%A4%AE%E0%A4%BF%E0%A4%B2_%E0%A4%AC%E0%A5%8B%E0%A4%B0%E0%A5%87%E0%A4%B2" title="एमिल बोरेल – Hindi" lang="hi" hreflang="hi" data-title="एमिल बोरेल" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – Ido" lang="io" hreflang="io" data-title="Émile Borel" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – Indonesian" lang="id" hreflang="id" data-title="Émile Borel" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – Italian" lang="it" hreflang="it" data-title="Émile Borel" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%9E%D7%99%D7%9C_%D7%91%D7%95%D7%A8%D7%9C" title="אמיל בורל – Hebrew" lang="he" hreflang="he" data-title="אמיל בורל" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%AD%D0%BC%D0%B8%D0%BB%D1%8C_%D0%91%D0%BE%D1%80%D0%B5%D0%BB%D1%8C" title="Эмиль Борель – Kazakh" lang="kk" hreflang="kk" data-title="Эмиль Борель" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Emile_Borel" title="Emile Borel – Haitian Creole" lang="ht" hreflang="ht" data-title="Emile Borel" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Emils_Borels" title="Emils Borels – Latvian" lang="lv" hreflang="lv" data-title="Emils Borels" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – Hungarian" lang="hu" hreflang="hu" data-title="Émile Borel" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mai mw-list-item"><a href="https://mai.wikipedia.org/wiki/%E0%A4%8F%E0%A4%AE%E0%A4%BF%E0%A4%B2_%E0%A4%AC%E0%A5%8B%E0%A4%B0%E0%A5%87%E0%A4%B2" title="एमिल बोरेल – Maithili" lang="mai" hreflang="mai" data-title="एमिल बोरेल" data-language-autonym="मैथिली" data-language-local-name="Maithili" class="interlanguage-link-target"><span>मैथिली</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%A7%D9%8A%D9%85%D9%8A%D9%84_%D8%A8%D9%88%D8%B1%D9%8A%D9%84" title="ايميل بوريل – Egyptian Arabic" lang="arz" hreflang="arz" data-title="ايميل بوريل" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – Dutch" lang="nl" hreflang="nl" data-title="Émile Borel" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%A8%E3%83%9F%E3%83%BC%E3%83%AB%E3%83%BB%E3%83%9C%E3%83%AC%E3%83%AB" title="エミール・ボレル – Japanese" lang="ja" hreflang="ja" data-title="エミール・ボレル" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Émile Borel" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Émile Borel" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Emili_Bor%C3%A8l" title="Emili Borèl – Occitan" lang="oc" hreflang="oc" data-title="Emili Borèl" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – Piedmontese" lang="pms" hreflang="pms" data-title="Émile Borel" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – Polish" lang="pl" hreflang="pl" data-title="Émile Borel" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – Portuguese" lang="pt" hreflang="pt" data-title="Émile Borel" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – Romanian" lang="ro" hreflang="ro" data-title="Émile Borel" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%91%D0%BE%D1%80%D0%B5%D0%BB%D1%8C,_%D0%AD%D0%BC%D0%B8%D0%BB%D1%8C" title="Борель, Эмиль – Russian" lang="ru" hreflang="ru" data-title="Борель, Эмиль" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – Slovak" lang="sk" hreflang="sk" data-title="Émile Borel" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – Slovenian" lang="sl" hreflang="sl" data-title="Émile Borel" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%95%D0%BC%D0%B8%D0%BB_%D0%91%D0%BE%D1%80%D0%B5%D0%BB" title="Емил Борел – Serbian" lang="sr" hreflang="sr" data-title="Емил Борел" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – Finnish" lang="fi" hreflang="fi" data-title="Émile Borel" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/%C3%89mile_Borel" title="Émile Borel – Swedish" lang="sv" hreflang="sv" data-title="Émile Borel" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%AD%D0%BC%D0%B8%D0%BB%D1%8C_%D0%91%D0%BE%D1%80%D0%B5%D0%BB%D1%8C" title="Эмиль Борель – Tatar" lang="tt" hreflang="tt" data-title="Эмиль Борель" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%AD%E0%B8%A1%E0%B8%B5%E0%B8%A5_%E0%B8%9A%E0%B8%AD%E0%B9%81%E0%B8%A3%E0%B8%A5" title="เอมีล บอแรล – Thai" 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</div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to 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i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Not to be confused with <a href="/wiki/Armand_Borel" title="Armand Borel">Armand Borel</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size: 100%;"><div class="fn" style="font-size:125%;">Émile Borel</div></th></tr><tr><td colspan="2" class="infobox-image"><span typeof="mw:File"><a href="/wiki/File:Emile_Borel-1932.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Emile_Borel-1932.jpg/200px-Emile_Borel-1932.jpg" decoding="async" width="200" height="269" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Emile_Borel-1932.jpg/300px-Emile_Borel-1932.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Emile_Borel-1932.jpg/400px-Emile_Borel-1932.jpg 2x" data-file-width="4166" data-file-height="5598" /></a></span><div class="infobox-caption" style="line-height:normal;padding-top:0.2em;">Émile Borel (1932)</div></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"></td></tr><tr><th colspan="2" class="infobox-header" style="color: #202122; background:lavender;line-height:normal;padding:0.2em;"><a href="/wiki/List_of_naval_ministers_of_France" title="List of naval ministers of France">Minister of the Navy</a></th></tr><tr><td colspan="2" class="infobox-full-data" style="border-bottom:none"><span class="nowrap"><b>In office</b></span><br />17 April 1925 – 28 November 1925</td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"></tr><tr><th scope="row" class="infobox-label" style="text-align:left"><span class="nowrap">Prime Minister</span></th><td class="infobox-data"><a href="/wiki/Paul_Painlev%C3%A9" title="Paul Painlevé">Paul Painlevé</a></td></tr><tr><th scope="row" class="infobox-label" style="text-align:left"><span class="nowrap">Preceded by</span></th><td class="infobox-data"><a href="/wiki/Jacques-Louis_Dumesnil" title="Jacques-Louis Dumesnil">Jacques-Louis Dumesnil</a></td></tr><tr><th scope="row" class="infobox-label" style="text-align:left"><span class="nowrap">Succeeded by</span></th><td class="infobox-data"><a href="/wiki/Georges_Leygues" title="Georges Leygues">Georges Leygues</a></td><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"></tr><tr><th colspan="2" class="infobox-header" style="color: #202122; background:lavender;line-height:normal;padding:0.2em;">Member of the <a href="/wiki/Chamber_of_Deputies_(France)" title="Chamber of Deputies (France)">Chamber of Deputies</a></th></tr><tr><td colspan="2" class="infobox-full-data" style="border-bottom:none"><span class="nowrap"><b>In office</b></span><br />15 June 1924 – 4 June 1936</td></tr><tr style="display:none"><td colspan="2"> </td></tr><tr><th colspan="2" class="infobox-header" style="color: #202122; background:lavender">Personal details</th></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><div style="display:inline" class="nickname">Félix Édouard Justin Émile Borel</div><br /><span style="display:none">(<span class="bday">1871-01-07</span>)</span>7 January 1871<br /><a href="/wiki/Saint-Affrique" title="Saint-Affrique">Saint-Affrique</a>, <a href="/wiki/France" title="France">France</a></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">3 February 1956<span style="display:none">(1956-02-03)</span> (aged 85)<br /><a href="/wiki/Paris" title="Paris">Paris</a>, <a href="/wiki/France" title="France">France</a></td></tr><tr><th scope="row" class="infobox-label">Nationality</th><td class="infobox-data"><a href="/wiki/French_people" title="French people">French</a> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"></td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><a href="/wiki/%C3%89cole_normale_sup%C3%A9rieure_(Paris)" title="École normale supérieure (Paris)">École normale supérieure Paris</a></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><a href="/wiki/Measure_theory" class="mw-redirect" title="Measure theory">Measure theory</a> <br /> <a href="/wiki/Probability_theory" title="Probability theory">Probability theory</a> <br /> <a href="/wiki/Heine%E2%80%93Borel_theorem" title="Heine–Borel theorem">Heine–Borel theorem</a></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"><b>Scientific career</b></td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category">Mathematics</td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><a href="/wiki/University_of_Paris" title="University of Paris">University of Paris</a></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Thesis" title="Thesis">Thesis</a></th><td class="infobox-data"><i><a rel="nofollow" class="external text" href="http://archive.numdam.org/ARCHIVE/ASENS/ASENS_1895_3_12_/ASENS_1895_3_12__9_0/ASENS_1895_3_12__9_0.pdf">Sur quelques points de la théorie des fonctions</a></i> <span style="font-size:97%;">(1893)</span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Doctoral_advisor" title="Doctoral advisor">Doctoral advisor</a></th><td class="infobox-data"><a href="/wiki/Jean_Gaston_Darboux" title="Jean Gaston Darboux">Gaston Darboux</a></td></tr><tr><th scope="row" class="infobox-label">Doctoral students</th><td class="infobox-data"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist"><ul><li><a href="/wiki/Paul_Dienes" title="Paul Dienes">Paul Dienes</a></li><li><a href="/wiki/Henri_Lebesgue" title="Henri Lebesgue">Henri Lebesgue</a></li><li><a href="/wiki/Paul_Montel" title="Paul Montel">Paul Montel</a></li><li><a href="/wiki/Georges_Valiron" title="Georges Valiron">Georges Valiron</a></li></ul></div></td></tr><tr style="display:none"><td colspan="2"> </td></tr><tr style="display:none"><td colspan="2"> </td></tr><tr><td colspan="2" class="infobox-below" style="border-top: 1px solid right;"><div></div></td></tr></tbody></table> <p><b>Félix Édouard Justin Émile Borel</b> (<style data-mw-deduplicate="TemplateStyles:r1177148991">.mw-parser-output .IPA-label-small{font-size:85%}.mw-parser-output .references .IPA-label-small,.mw-parser-output .infobox .IPA-label-small,.mw-parser-output .navbox .IPA-label-small{font-size:100%}</style><span class="IPA-label IPA-label-small">French:</span> <span class="IPA nowrap" lang="fr-Latn-fonipa"><a href="/wiki/Help:IPA/French" title="Help:IPA/French">[bɔʁɛl]</a></span>; 7 January 1871 – 3 February 1956)<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> was a <a href="/wiki/French_people" title="French people">French</a> <a href="/wiki/Mathematician" title="Mathematician">mathematician</a><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Politician" title="Politician">politician</a>. As a mathematician, he was known for his founding work in the areas of <a href="/wiki/Measure_theory" class="mw-redirect" title="Measure theory">measure theory</a> and <a href="/wiki/Probability" title="Probability">probability</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Biography">Biography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%89mile_Borel&action=edit&section=1" title="Edit section: Biography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Borel was born in <a href="/wiki/Saint-Affrique" title="Saint-Affrique">Saint-Affrique</a>, <a href="/wiki/Aveyron" title="Aveyron">Aveyron</a>, the son of a <a href="/wiki/Protestant" class="mw-redirect" title="Protestant">Protestant</a> pastor.<sup id="cite_ref-McElroy_2009_3-0" class="reference"><a href="#cite_note-McElroy_2009-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> He studied at the <a href="/wiki/Coll%C3%A8ge_Sainte-Barbe" title="Collège Sainte-Barbe">Collège Sainte-Barbe</a> and <a href="/wiki/Lyc%C3%A9e_Louis-le-Grand" title="Lycée Louis-le-Grand">Lycée Louis-le-Grand</a> before applying to both the <a href="/wiki/%C3%89cole_normale_sup%C3%A9rieure_(Paris)" title="École normale supérieure (Paris)">École normale supérieure</a> and the <a href="/wiki/%C3%89cole_Polytechnique" class="mw-redirect" title="École Polytechnique">École Polytechnique</a>. He qualified in the first position for both and chose to attend the former institution in 1889. That year he also won the <a href="/wiki/Concours_g%C3%A9n%C3%A9ral" title="Concours général">concours général</a>, an annual national mathematics competition. After graduating in 1892, he placed first in the <a href="/wiki/Agr%C3%A9gation" title="Agrégation">agrégation</a>, a competitive civil service examination leading to the position of professeur agrégé. His thesis, published in 1893, was titled <i>Sur quelques points de la théorie des fonctions</i> ("On some points in the theory of functions"). That year, Borel started a four-year stint as a lecturer at the <a href="/wiki/University_of_Lille" title="University of Lille">University of Lille</a>, during which time he published 22 research papers. He returned to the École normale supérieure in 1897, and was appointed to the chair of theory of functions, which he held until 1941.<sup id="cite_ref-Chang_2011_4-0" class="reference"><a href="#cite_note-Chang_2011-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>In 1901, Borel married 17-year-old Marguerite, the daughter of colleague <a href="/wiki/Paul_%C3%89mile_Appel" class="mw-redirect" title="Paul Émile Appel">Paul Émile Appel</a>; she later wrote more than 30 novels under the pseudonym <a href="/wiki/Camille_Marbo" title="Camille Marbo">Camille Marbo</a>. Émile Borel died in Paris on 3 February 1956.<sup id="cite_ref-Chang_2011_4-1" class="reference"><a href="#cite_note-Chang_2011-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Work">Work</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%89mile_Borel&action=edit&section=2" title="Edit section: Work"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Along with <a href="/wiki/Ren%C3%A9-Louis_Baire" title="René-Louis Baire">René-Louis Baire</a> and <a href="/wiki/Henri_Lebesgue" title="Henri Lebesgue">Henri Lebesgue</a>, Émile Borel was among the pioneers of <a href="/wiki/Measure_(mathematics)" title="Measure (mathematics)">measure theory</a> and its application to <a href="/wiki/Probability_theory" title="Probability theory">probability theory</a>. The concept of a <a href="/wiki/Borel_set" title="Borel set">Borel set</a> is named in his honor. One of his books on probability introduced the amusing <a href="/wiki/Thought_experiment" title="Thought experiment">thought experiment</a> that entered popular culture under the name <a href="/wiki/Infinite_monkey_theorem" title="Infinite monkey theorem">infinite monkey theorem</a> or the like. He also published a series of papers (1921–1927) that first defined <a href="/wiki/Game_theory" title="Game theory">games of strategy</a>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> John von Neumann objected to this assignment of priority in a letter to <i>Econometrica</i> published in 1953 where he asserted that Borel could not have defined games of strategy because he rejected the minimax theorem.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>With the development of <a href="/wiki/Statistical_hypothesis_testing" class="mw-redirect" title="Statistical hypothesis testing">statistical hypothesis testing</a> in the early 1900s various tests for <a href="/wiki/Randomness" title="Randomness">randomness</a> were proposed. Sometimes these were claimed to have some kind of general significance, but mostly they were just viewed as simple practical methods. In 1909, Borel formulated the notion that numbers picked randomly on the basis of their value are <a href="/wiki/Almost_always" class="mw-redirect" title="Almost always">almost always</a> <a href="/wiki/Normal_number" title="Normal number">normal</a>, and with explicit constructions in terms of digits, it is quite straightforward to get numbers that are normal.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>In 1913 and 1914 he bridged the gap between <a href="/wiki/Hyperbolic_geometry" title="Hyperbolic geometry">hyperbolic geometry</a> and <a href="/wiki/Special_relativity" title="Special relativity">special relativity</a> with expository work. For instance, his book <i>Introduction Géométrique à quelques Théories Physiques</i><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> described <a href="/wiki/Hyperbolic_rotation" class="mw-redirect" title="Hyperbolic rotation">hyperbolic rotations</a> as transformations that leave a hyperbola <a href="/wiki/Invariant_(mathematics)#Invariant_set" title="Invariant (mathematics)">stable</a> just as a circle around a rotational center is stable. </p><p>In 1922, he founded the <a href="/wiki/Paris_Institute_of_Statistics" title="Paris Institute of Statistics">Paris Institute of Statistics</a>, the oldest French school for statistics; then in 1928 he co-founded the <a href="/wiki/Institut_Henri_Poincar%C3%A9" title="Institut Henri Poincaré">Institut Henri Poincaré</a> in Paris. </p> <div class="mw-heading mw-heading2"><h2 id="Political_career">Political career</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%89mile_Borel&action=edit&section=3" title="Edit section: Political career"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the 1920s, 1930s, and 1940s, he was active in politics. From 1924 to 1936, he was a member of the <a href="/wiki/Chamber_of_Deputies_(France)" title="Chamber of Deputies (France)">Chamber of Deputies</a>.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> In 1925, he was <a href="/wiki/List_of_Naval_Ministers_of_France" class="mw-redirect" title="List of Naval Ministers of France">Minister of the Navy</a> in the cabinet of fellow mathematician <a href="/wiki/Paul_Painlev%C3%A9" title="Paul Painlevé">Paul Painlevé</a>. During the <a href="/wiki/Second_World_War" class="mw-redirect" title="Second World War">Second World War</a>, he was a member of the <a href="/wiki/French_Resistance" title="French Resistance">French Resistance</a>. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:1918_E_Borel.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/1918_E_Borel.jpg/220px-1918_E_Borel.jpg" decoding="async" width="220" height="293" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/1918_E_Borel.jpg/330px-1918_E_Borel.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/33/1918_E_Borel.jpg/440px-1918_E_Borel.jpg 2x" data-file-width="1354" data-file-height="1805" /></a><figcaption><a href="/wiki/Autochrome_Lumi%C3%A8re" title="Autochrome Lumière">Autochrome</a> portrait by <a href="/wiki/The_Archives_of_the_Planet" title="The Archives of the Planet">Auguste Léon</a>, 1918</figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="Honors">Honors</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%89mile_Borel&action=edit&section=4" title="Edit section: Honors"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Besides the <i>Centre Émile Borel</i> at the <a href="/wiki/Institut_Henri_Poincar%C3%A9" title="Institut Henri Poincaré">Institut Henri Poincaré</a> in Paris and a <a href="/wiki/Borel_(crater)" title="Borel (crater)">crater on the Moon</a>, the following mathematical notions are named after him: </p> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 25em;"> <ul><li><a href="/wiki/Borel_algebra" class="mw-redirect" title="Borel algebra">Borel algebra</a></li> <li><a href="/wiki/Borel%27s_lemma" title="Borel's lemma">Borel's lemma</a></li> <li><a href="/wiki/Borel%27s_law_of_large_numbers" class="mw-redirect" title="Borel's law of large numbers">Borel's law of large numbers</a></li> <li><a href="/wiki/Borel_measure" title="Borel measure">Borel measure</a></li> <li><a href="/wiki/Borel%E2%80%93Kolmogorov_paradox" title="Borel–Kolmogorov paradox">Borel–Kolmogorov paradox</a></li> <li><a href="/wiki/Borel%E2%80%93Cantelli_lemma" title="Borel–Cantelli lemma">Borel–Cantelli lemma</a></li> <li><a href="/wiki/Borel%E2%80%93Carath%C3%A9odory_theorem" title="Borel–Carathéodory theorem">Borel–Carathéodory theorem</a></li> <li><a href="/wiki/Heine%E2%80%93Borel_theorem" title="Heine–Borel theorem">Heine–Borel theorem</a></li> <li><a href="/wiki/Borel_determinacy_theorem" title="Borel determinacy theorem">Borel determinacy theorem</a></li> <li><a href="/wiki/Borel_right_process" title="Borel right process">Borel right process</a></li> <li><a href="/wiki/Borel_set" title="Borel set">Borel set</a></li> <li><a href="/wiki/Borel_summation" title="Borel summation">Borel summation</a></li> <li><a href="/wiki/Borel_distribution" title="Borel distribution">Borel distribution</a></li> <li><a href="/wiki/Strong_measure_zero_set" title="Strong measure zero set">Borel's conjecture</a> about <a href="/wiki/Strong_measure_zero_set" title="Strong measure zero set">strong measure zero sets</a> (not to be confused with <a href="/wiki/Borel_conjecture" title="Borel conjecture">Borel conjecture</a>, named for Armand Borel).</li></ul> </div> <p>Borel also described a <a href="/wiki/Poker" title="Poker">poker</a> model that he coins <i>La Relance</i> in his 1938 book <i>Applications de la théorie des probabilités aux Jeux de Hasard</i>.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>Borel was awarded the <a href="/wiki/Resistance_Medal" title="Resistance Medal">Resistance Medal</a> in 1950.<sup id="cite_ref-Chang_2011_4-2" class="reference"><a href="#cite_note-Chang_2011-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Works">Works</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%89mile_Borel&action=edit&section=5" title="Edit section: Works"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1184024115"><div class="div-col" style="column-width: 25em;"> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li><i>On a few points about the theory of functions</i> (PhD thesis, 1894)</li> <li><i>Introduction to the study of <a href="/wiki/Number_theory" title="Number theory">number theory</a> and superior algebra</i> (1895)</li> <li><i>A course on the theory of functions</i> (1898)</li> <li><i>A course on <a href="/wiki/Power_series" title="Power series">power series</a></i> (1900)</li> <li><i>A course on <a href="/wiki/Divergent_series" title="Divergent series">divergent series</a></i> (1901)</li> <li><i>A course on positive terms series</i> (1902)</li> <li><i>A course on <a href="/wiki/Meromorphic_functions" class="mw-redirect" title="Meromorphic functions">meromorphic functions</a></i> (1903)</li> <li><i>A course on growth theory at the Paris faculty of sciences</i> (1910)</li> <li><i>A course on functions of a real variable and polynomial serial developments</i> (1905)</li> <li><i>Chance</i> (1914)</li> <li><i>Geometrical introduction to some physical theories</i> (1914)</li> <li><i>A course on <a href="/wiki/Complex_variable" class="mw-redirect" title="Complex variable">complex variable</a> uniform monogenic functions</i> (1917)</li> <li><i>On the method in sciences</i> (1919)</li> <li><i>Space and time</i> (1921)</li> <li><i><a href="/wiki/Game_theory" title="Game theory">Game theory</a> and left symmetric core integral equations</i> (1921)</li> <li><i>Methods and problems of the theory of functions</i> (1922)</li> <li><i>Space and time</i> (1922)</li> <li><i>A treatise on probability calculation and its applications</i> (1924–1934)</li> <li><i>Application of <a href="/wiki/Probability_theory" title="Probability theory">probability theory</a> to <a href="/wiki/Games_of_chance" class="mw-redirect" title="Games of chance">games of chance</a></i> (1938)</li> <li><i>Principles and classical formulas for probability calculation</i> (1925)</li> <li><i>Practical and philosophical values of probabilities</i> (1939)</li> <li><i>Mathematical theory of contract bridge for everyone</i> (1940)</li> <li><i>Game, luck and contemporary scientific theories</i> (1941)</li> <li><i>Probabilities and life</i> (1943)</li> <li><i>Evolution of <a href="/wiki/Mechanics" title="Mechanics">mechanics</a></i> (1943)</li> <li><i>Paradoxes of the infinite</i> (1946)</li> <li><i>Elements of <a href="/wiki/Set_theory" title="Set theory">set theory</a></i> (1949)</li> <li><i>Probability and certainty</i> (1950)</li> <li><i>Inaccessible numbers</i> (1952)</li> <li><i>Imaginary and real in mathematics and physics</i> (1952)</li> <li><i><a href="/wiki/Emile_Borel" class="mw-redirect" title="Emile Borel">Emile Borel</a> complete works</i> (1972)</li></ul> </div> </div> <div class="mw-heading mw-heading2"><h2 id="Articles">Articles</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%89mile_Borel&action=edit&section=6" title="Edit section: Articles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="languageicon">(in French)</span> <a rel="nofollow" class="external text" href="http://amshistorica.unibo.it/diglib.php?inv=7&int_ptnum=51&term_ptnum=107&format=jpg">"<i>La science est-elle responsable de la crise mondiale?</i>"</a>, <a href="/wiki/Scientia_(Italian_journal)" title="Scientia (Italian journal)">Scientia : rivista internazionale di sintesi scientifica</a>, 51, 1932, pp. 99–106.</li> <li><span class="languageicon">(in French)</span> <a rel="nofollow" class="external text" href="http://amshistorica.unibo.it/diglib.php?inv=7&int_ptnum=31&term_ptnum=231&format=jpg">"<i>La science dans une société socialiste</i>"</a>, Scientia : rivista internazionale di sintesi scientifica, 31, 1922, pp. 223–228.</li> <li><span class="languageicon">(in French)</span> <a rel="nofollow" class="external text" href="http://amshistorica.unibo.it/diglib.php?inv=6&int_ptnum=6&term_ptnum=29&format=jpg">"<i>Le continu mathématique et le continu physique</i>"</a>, <a href="/wiki/Scientia_(Italian_journal)" title="Scientia (Italian journal)">Rivista di scienza</a>, 6, 1909, pp. 21–35.</li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%89mile_Borel&action=edit&section=7" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Borel_right_process" title="Borel right process">Borel right process</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%89mile_Borel&action=edit&section=8" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFMay1970–1980" class="citation encyclopaedia cs1">May, Kenneth (1970–1980). "Borel, Émile". <i><a href="/wiki/Dictionary_of_Scientific_Biography" title="Dictionary of Scientific Biography">Dictionary of Scientific Biography</a></i>. Vol. 2. New York: Charles Scribner's Sons. pp. 302–305. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-684-10114-9" title="Special:BookSources/978-0-684-10114-9"><bdi>978-0-684-10114-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Borel%2C+%C3%89mile&rft.btitle=Dictionary+of+Scientific+Biography&rft.place=New+York&rft.pages=302-305&rft.pub=Charles+Scribner%27s+Sons&rft.date=1970%2F1980&rft.isbn=978-0-684-10114-9&rft.aulast=May&rft.aufirst=Kenneth&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%C3%89mile+Borel" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.univ-lille1.fr/asa_2/mathematiques/mathematiques-2.htm">Émile Borel's biography</a> – <a href="/wiki/Universit%C3%A9_Lille_Nord_de_France" class="mw-redirect" title="Université Lille Nord de France">Université Lille Nord de France</a></span> </li> <li id="cite_note-McElroy_2009-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-McElroy_2009_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcElroy,_Tucker2009" class="citation book cs1">McElroy, Tucker (2009). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=MiZIWtX9AJUC&pg=PA46"><i>A to Z of Mathematicians</i></a>. Infobase Publishing. p. 46. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4381-0921-3" title="Special:BookSources/978-1-4381-0921-3"><bdi>978-1-4381-0921-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+to+Z+of+Mathematicians&rft.pages=46&rft.pub=Infobase+Publishing&rft.date=2009&rft.isbn=978-1-4381-0921-3&rft.au=McElroy%2C+Tucker&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DMiZIWtX9AJUC%26pg%3DPA46&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%C3%89mile+Borel" class="Z3988"></span></span> </li> <li id="cite_note-Chang_2011-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-Chang_2011_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Chang_2011_4-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Chang_2011_4-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChang,_Sooyoung2011" class="citation book cs1">Chang, Sooyoung (2011). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=4siw31DPONUC&pg=PA107"><i>Academic Genealogy of Mathematicians</i></a>. World Scientific. p. 107. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-981-4282-29-1" title="Special:BookSources/978-981-4282-29-1"><bdi>978-981-4282-29-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Academic+Genealogy+of+Mathematicians&rft.pages=107&rft.pub=World+Scientific&rft.date=2011&rft.isbn=978-981-4282-29-1&rft.au=Chang%2C+Sooyoung&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D4siw31DPONUC%26pg%3DPA107&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%C3%89mile+Borel" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.britannica.com/EBchecked/topic/74060/Emile-Borel">"Émile Borel," <i>Encyclopædia Britannica</i></a></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFvon_NeumannFréchet1953" class="citation journal cs1">von Neumann, J.; Fréchet, M. (1953). <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/1906950">"Communication on the Borel Notes"</a>. <i>Econometrica</i>. <b>21</b> (1): 124–127. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F1906950">10.2307/1906950</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0012-9682">0012-9682</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/1906950">1906950</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Econometrica&rft.atitle=Communication+on+the+Borel+Notes&rft.volume=21&rft.issue=1&rft.pages=124-127&rft.date=1953&rft.issn=0012-9682&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1906950%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.2307%2F1906950&rft.aulast=von+Neumann&rft.aufirst=J.&rft.au=Fr%C3%A9chet%2C+M.&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1906950&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%C3%89mile+Borel" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHarman2002" class="citation cs2">Harman, Glyn (2002), <a rel="nofollow" class="external text" href="https://books.google.com/books?id=RWC1DwAAQBAJ&pg=PA57">"One hundred years of normal numbers"</a>, in Bennett, M. A.; Berndt, B. C.; Boston, N.; Diamond, H. G.; Hildebrand, A. J.; Philipp, W. (eds.), <i>Surveys in Number Theory: Papers from the Millennial Conference on Number Theory</i>, A K Peters, pp. 57–74, <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=1956249">1956249</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=One+hundred+years+of+normal+numbers&rft.btitle=Surveys+in+Number+Theory%3A+Papers+from+the+Millennial+Conference+on+Number+Theory&rft.pages=57-74&rft.pub=A+K+Peters&rft.date=2002&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D1956249%23id-name%3DMR&rft.aulast=Harman&rft.aufirst=Glyn&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DRWC1DwAAQBAJ%26pg%3DPA57&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%C3%89mile+Borel" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">Émile Borel (1914) <a rel="nofollow" class="external text" href="http://ebooks.library.cornell.edu/cgi/t/text/text-idx?c=math;cc=math;view=toc;subview=short;idno=04710001">Introduction Geometrique à quelques Théories Physiques</a>, Gauthier-Villars, link from <a href="/wiki/Cornell_University" title="Cornell University">Cornell University</a> Historical Math Monographs</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.britannica.com/biography/Emile-Borel">"Émile Borel | French mathematician | Britannica"</a>. <i>www.britannica.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2023-03-12</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=www.britannica.com&rft.atitle=%C3%89mile+Borel+%7C+French+mathematician+%7C+Britannica&rft_id=https%3A%2F%2Fwww.britannica.com%2Fbiography%2FEmile-Borel&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%C3%89mile+Borel" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">Émile Borel and Jean Ville. Applications de la théorie des probabilités aux jeux de hasard. Gauthier-Vilars, 1938</span> </li> </ol></div></div> <ul><li>Michel Pinault, <i>Emile Borel, une carrière intellectuelle sous la 3ème République</i>, Paris, L'Harmattan, 2017. Voir : michel-pinault.over-blog.com</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C3%89mile_Borel&action=edit&section=9" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wikiquote-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/13px-Wikiquote-logo.svg.png" decoding="async" width="13" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/20px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/27px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></a></span> Quotations related to <a href="https://en.wikiquote.org/wiki/Special:Search/%C3%89mile_Borel" class="extiw" title="wikiquote:Special:Search/Émile Borel">Émile Borel</a> at Wikiquote</li> <li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Wikisource-logo.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png" decoding="async" width="12" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/18px-Wikisource-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/24px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /></a></span> French <a href="/wiki/Wikisource" title="Wikisource">Wikisource</a> has original text related to this article: <a href="https://en.wikisource.org/wiki/fr:Auteur:%C3%89mile_Borel" class="extiw" title="s:fr:Auteur:Émile Borel">Auteur:Émile Borel</a></li> <li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Media related to <a href="https://commons.wikimedia.org/wiki/Category:%C3%89mile_Borel_(mathematician)" class="extiw" title="commons:Category:Émile Borel (mathematician)">Émile Borel (mathematician)</a> at Wikimedia Commons</li> <li><a rel="nofollow" class="external text" href="https://archive.org/search.php?query=%28%28%28%22Émile%22%20OR%20Emile%29%20AND%20%28%22Borel%22%20OR%20Borel%29%29%20OR%20%28%221871-1956%22%20AND%20Borel%29%29%20AND%20%28-mediatype:software%29">Works by or about Émile Borel</a> at the <a href="/wiki/Internet_Archive" title="Internet Archive">Internet Archive</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFO'ConnorRobertson" class="citation cs2">O'Connor, John J.; <a href="/wiki/Edmund_F._Robertson" title="Edmund F. Robertson">Robertson, Edmund F.</a>, <a rel="nofollow" class="external text" href="https://mathshistory.st-andrews.ac.uk/Biographies/Borel.html">"Émile Borel"</a>, <i><a href="/wiki/MacTutor_History_of_Mathematics_Archive" title="MacTutor History of Mathematics Archive">MacTutor History of Mathematics Archive</a></i>, <a href="/wiki/University_of_St_Andrews" title="University of St Andrews">University of St Andrews</a></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=%C3%89mile+Borel&rft.btitle=MacTutor+History+of+Mathematics+Archive&rft.pub=University+of+St+Andrews&rft.aulast=O%27Connor&rft.aufirst=John+J.&rft.au=Robertson%2C+Edmund+F.&rft_id=https%3A%2F%2Fmathshistory.st-andrews.ac.uk%2FBiographies%2FBorel.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3A%C3%89mile+Borel" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:borel.emile">Author profile</a> in the database <a href="/wiki/Zentralblatt_MATH" class="mw-redirect" title="Zentralblatt MATH">zbMATH</a></li></ul> <table class="wikitable succession-box noprint" style="margin:0.5em auto; font-size:small;clear:both;"> <tbody><tr> <th colspan="3" style="border-top: 5px solid #ccccff;">Political offices </th></tr> <tr style="text-align:center;"> <td style="width:30%;" rowspan="1">Preceded by<div style="font-weight: bold"><a href="/wiki/Jacques-Louis_Dumesnil" title="Jacques-Louis Dumesnil">Jacques-Louis Dumesnil</a></div> </td> <td style="width: 40%; text-align: center;" rowspan="1"><b> <a href="/wiki/List_of_naval_ministers_of_France" title="List of naval ministers of France">Minister of the Navy</a> </b><br />April 17, 1925 – November 28, 1925 </td> <td style="width: 30%; text-align: center;" rowspan="1">Succeeded by<div style="font-weight: bold"><a href="/wiki/Georges_Leygues" title="Georges Leygues">Georges Leygues</a></div> </td></tr> </tbody></table> <p><br /> </p> <div 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href="https://id.oclc.org/worldcat/entity/E39PBJfGV4jMThkjY3kXXctHYP">WorldCat</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/118975528">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/n81041810">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb12088647b">France</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb12088647b">BnF data</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00520177">Japan</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://nla.gov.au/anbd.aut-an35115971">Australia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=skuk0000144&CON_LNG=ENG">Czech Republic</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://catalogo.bne.es/uhtbin/authoritybrowse.cgi?action=display&authority_id=XX900754">Spain</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.bnportugal.gov.pt/aut/catbnp/39218">Portugal</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://data.bibliotheken.nl/id/thes/p070334471">Netherlands</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://authority.bibsys.no/authority/rest/authorities/html/90261008">Norway</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://kopkatalogs.lv/F?func=direct&local_base=lnc10&doc_number=000058605&P_CON_LNG=ENG">Latvia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://katalog.nsk.hr/F/?func=direct&doc_number=000095667&local_base=nsk10">Croatia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.nlg.gr/cgi-bin/koha/opac-authoritiesdetail.pl?authid=246531">Greece</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://libris.kb.se/ljx02sv42641dsd">Sweden</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://dbn.bn.org.pl/descriptor-details/9810642948105606">Poland</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007258824405171">Israel</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://cantic.bnc.cat/registre/981058519505006706">Catalonia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://opac.kbr.be/LIBRARY/doc/AUTHORITY/14266600">Belgium</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Academics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://ci.nii.ac.jp/author/DA02769870?l=en">CiNii</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.mathgenealogy.org/id.php?id=39071">Mathematics Genealogy Project</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:borel.emile">zbMATH</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet/MRAuthorID/250357">MathSciNet</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www2.assemblee-nationale.fr/sycomore/fiche/(num_dept)/975">Sycomore</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://trove.nla.gov.au/people/831153">Trove</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-biographie.de/pnd118975528.html?language=en">Deutsche Biographie</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-digitale-bibliothek.de/person/gnd/118975528">DDB</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.idref.fr/029212871">IdRef</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://snaccooperative.org/ark:/99166/w6p023ts">SNAC</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Émile_Borel&oldid=1241454404">https://en.wikipedia.org/w/index.php?title=Émile_Borel&oldid=1241454404</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a 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