CINXE.COM

<!DOCTYPE html> <html class="client-nojs" lang="en" dir="ltr"> <head> <meta charset="UTF-8"/> <title>Encyclopedia of Mathematics</title> <script>document.documentElement.className="client-js";RLCONF={"wgBreakFrames":!1,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy","wgMonthNames":["","January","February","March","April","May","June","July","August","September","October","November","December"],"wgRequestId":"670a3c101978a06770319b50","wgCSPNonce":!1,"wgCanonicalNamespace":"","wgCanonicalSpecialPageName":!1,"wgNamespaceNumber":0,"wgPageName":"Main_Page","wgTitle":"Main Page","wgCurRevisionId":45949,"wgRevisionId":45949,"wgArticleId":1,"wgIsArticle":!0,"wgIsRedirect":!1,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":[],"wgPageContentLanguage":"en","wgPageContentModel":"wikitext","wgRelevantPageName":"Main_Page","wgRelevantArticleId":1,"wgIsProbablyEditable":!1,"wgRelevantPageIsProbablyEditable":!1,"wgRestrictionEdit":["sysop"],"wgRestrictionMove":["sysop"],"wgIsMainPage":!0,"wgMjSize":100};RLSTATE={"site.styles":"ready","noscript": "ready","user.styles":"ready","user":"ready","user.options":"loading"};RLPAGEMODULES=["ext.MjCDN","site","mediawiki.page.startup","mediawiki.page.ready"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.implement("user.options@1hzgi",function($,jQuery,require,module){/*@nomin*/mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); });});</script> <script async="" src="/load.php?lang=en&modules=startup&only=scripts&raw=1&skin=springereom"></script> <link rel="stylesheet" href="/skins/springereom/main-ltr.css?486a0" media="screen"/> <meta name="generator" content="MediaWiki 1.35.13"/> <link rel="shortcut icon" href="/favicon.ico"/> <link rel="search" type="application/opensearchdescription+xml" href="/opensearch_desc.php" title="Encyclopedia of Mathematics (en)"/> <link rel="EditURI" type="application/rsd+xml" href="https://encyclopediaofmath.org/api.php?action=rsd"/>   </head> <body class="mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Main_Page rootpage-Main_Page skin-springereom action-view"><div id="OuterShell"><div id="InnerShell"><a id="top"></a> <div id="head" class="noprint"> <div id="headInner"> <a id="mainpagelink" href="/" > </a> <div id="p-personal"> <ul> <li id="pt-anonlogin"><a href="/index.php?title=Special:UserLogin&returnto=Main+Page">Log in</a></li> </ul> </div>  <div id="p-search"> <form action="/index.php" id="searchform"> <input type='hidden' name="title" value="Special:Search"/> <div id="simpleSearch"> <input id="searchInput" name="search" type="text" value="" /> <button id="searchButton" type='submit' name='button' ><img src="/skins/springereom/images/search-rtl.png" alt="Search"/></button> </div> </form> </div>  <p id="MetaLogos"> <a href="http://www.springer.com" id="Springercom"><span>www.springer.com</span></a> <a href="http://www.euro-math-soc.eu/" id="Euromathsoc"><span>The European Mathematical Society</span></a> </p> </div> </div> <div id="ContentShell"> <div id="mw-panel" class="noprint">  <div class="portal" id='p-navigation'> <h5>Navigation</h5> <div class="body"> <ul> <li id="n-mainpage-description"><a href="/wiki/Main_Page" title="Visit the main page [z]" accesskey="z">Main page</a></li> <li id="n-Pages-A-Z"><a href="/wiki/Special:AllPages">Pages A-Z</a></li> <li id="n-StatProb-Collection"><a href="/wiki/Category:Statprob">StatProb Collection</a></li> <li id="n-recentchanges"><a href="/wiki/Special:RecentChanges" title="A list of recent changes in the wiki [r]" accesskey="r">Recent changes</a></li> <li id="n-currentevents"><a href="/wiki/Encyclopedia_of_Mathematics:Current_events" title="Find background information on current events">Current events</a></li> <li id="n-randompage"><a href="/wiki/Special:Random" title="Load a random page [x]" accesskey="x">Random page</a></li> <li id="n-help"><a href="/wiki/Help:Contents" title="The place to find out">Help</a></li> <li id="n-Project-talk"><a href="/wiki/Talk:EoM:This_project">Project talk</a></li> <li id="n-Request-account"><a href="/wiki/Special:RequestAccount">Request account</a></li> </ul> </div> </div>     <div class="portal" id='p-tb'> <h5>Tools</h5> <div class="body"> <ul> <li id="t-whatlinkshere"><a href="/wiki/Special:WhatLinksHere/Main_Page" title="A list of all wiki pages that link here [j]" accesskey="j">What links here</a></li> <li id="t-recentchangeslinked"><a href="/wiki/Special:RecentChangesLinked/Main_Page" rel="nofollow" title="Recent changes in pages linked from this page [k]" accesskey="k">Related changes</a></li> <li id="t-specialpages"><a href="/wiki/Special:SpecialPages" title="A list of all special pages [q]" accesskey="q">Special pages</a></li> <li id="t-print"><a href="javascript:print();" rel="alternate" title="Printable version of this page [p]" accesskey="p">Printable version</a></li> <li id="t-permalink"><a href="/index.php?title=Main_Page&oldid=45949" title="Permanent link to this revision of the page">Permanent link</a></li> <li id="t-info"><a href="/index.php?title=Main_Page&action=info" title="More information about this page">Page information</a></li> </ul> </div> </div>    </div>  <div id="content"> <div id="ContentNavigation" class="noprint"> <div id="left-navigation">  <div id="p-namespaces" class="springereomTabs"> <h5>Namespaces</h5> <ul> <li id="ca-nstab-main" class="selected"><a href="/wiki/Main_Page" title="View the content page [c]" accesskey="c"><span>Main page</span></a></li> <li id="ca-talk"><a href="/wiki/Talk:Main_Page" title="Discussion about the content page [t]" accesskey="t"><span>Discussion</span></a></li> </ul> </div>   <div id="p-variants" class="springereomMenu emptyPortlet"> <h5><span>Variants</span><a href="#"></a></h5> <div class="menu"> <ul> </ul> </div> </div>  </div> <div id="right-navigation">  <div id="p-views" class="springereomTabs"> <h5>Views</h5> <ul> <li id="ca-view" class="selected"><a href="/wiki/Main_Page" ><span>View</span></a></li> <li id="ca-viewsource"><a href="/index.php?title=Main_Page&action=edit" title="This page is protected.
You can view its source [e]" accesskey="e"><span>View source</span></a></li> <li id="ca-history" class="collapsible"><a href="/index.php?title=Main_Page&action=history" title="Past revisions of this page [h]" accesskey="h"><span>History</span></a></li> </ul> </div>   <div id="p-cactions" class="springereomMenu emptyPortlet"> <h5><span>Actions</span><a href="#"></a></h5> <div class="menu"> <ul> </ul> </div> </div>  </div> </div> <div id="InnerContent"> <div id="mw-js-message" style="display:none;"></div>  <h1 id="firstHeading" class="firstHeading">Main Page</h1>   <div id="bodyContent">  <div id="siteSub">From Encyclopedia of Mathematics</div>   <div id="contentSub"></div>   <div id="jump-to-nav"> Jump to: <a href="#mw-head">navigation</a>, <a href="#p-search">search</a> </div>   <div id="mw-content-text" lang="en" dir="ltr" class="mw-content-ltr"><div class="mw-parser-output"><h2><span class="mw-headline" id="Important_Notification"><b>Important Notification</b></span></h2> <p><b>Move of The Encyclopedia of Mathematics from Springer Verlag to EMS Press</b> </p> <ul><li><i>The Encyclopedia of Mathematics (EoM) has moved from <a rel="nofollow" class="external text" href="https://www.springer.com/de">Springer Verlag</a> to <a rel="nofollow" class="external text" href="https://ems.press/">EMS Press</a>, the Berlin-based mathematics publisher, owned by the <a rel="nofollow" class="external text" href="https://euro-math-soc.eu/">European Mathematical Society</a>.</i></li></ul> <ul><li><i>Therefore, the software of this server was updated - see the <a href="/wiki/Special:Version" title="Special:Version">Special:Version</a> for details.</i></li></ul> <ul><li><i>In case you encounter any problems with the new software just drop a note on the <a href="/wiki/Talk:Main_Page" title="Talk:Main Page"> discussion page</a> of this page.</i></li></ul> <ul><li><i>Further Information will be posted here soon, in particular concerning the licensing agreement.</i></li></ul> <p><b>Please stay tuned with EoM!</b> </p> <h2><span class="mw-headline" id=""></span></h2> <p>The Encyclopedia of Mathematics wiki is an open access resource designed specifically for the mathematics community. The original articles are from the online Encyclopaedia of Mathematics, published by Kluwer Academic Publishers in 2002. With more than 8,000 entries, illuminating nearly 50,000 notions in mathematics, the Encyclopaedia of Mathematics was the most up-to-date graduate-level reference work in the field of mathematics. </p><p>Springer, in cooperation with the European Mathematical Society, has made the content of this Encyclopedia freely open to the public. It is hoped that the mathematics community will find it useful and will be motivated to update those topics that fall within their own expertise or add new topics enabling the wiki to become yet again the most comprehensive and up-to-date online mathematics reference work. </p><p>The original articles from the Encyclopaedia of Mathematics remain copyrighted to Springer but any new articles added and any changes made to existing articles within encyclopediaofmath.org will come under the <a rel="nofollow" class="external text" href="http://creativecommons.org/licenses/by-sa/3.0/">Creative Commons Attribution Share-Alike License</a>. An <a href="/wiki/Editorial_Board" title="Editorial Board">editorial board</a>, under the management of the European Mathematical Society, monitors any changes to articles and has full scientific authority over alterations and deletions. </p><p>This wiki is a <a class="external text" href="http://www.mediawiki.org/wiki/MediaWiki">MediaWiki</a> that uses the <a rel="nofollow" class="external text" href="http://www.mathjax.org/">MathJax</a> extension, making it possible to insert mathematical equations in <a rel="nofollow" class="external text" href="http://en.wikipedia.org/wiki/TeX">$\rm \TeX$</a> and <a rel="nofollow" class="external text" href="http://en.wikipedia.org/wiki/LaTeX">$\rm \LaTeX$</a>. For instructions on how this can be achieved, please see the <a href="/wiki/Help" class="mw-redirect" title="Help">Help page</a>. </p><p><br /> </p> <table cellspacing="0" cellpadding="0" align="center" style="width:100%; border:2px #a3b1bf solid; background:#f5faff; text-align:center;"> <tbody><tr> <td align="center" style="width:50%; padding:5px 2%;" valign="top"> <p><span style="font-size: 140%;"><a href="/wiki/Editorial_Board" title="Editorial Board"> Editorial Board</a></span><br /> </p> </td> <td align="center" style="width:50%; padding:5px 2%;" valign="top"> <p><span style="font-size: 140%;"><a href="/wiki/Encyclopedia_of_Mathematics:Policy" title="Encyclopedia of Mathematics:Policy"> Editorial Policy</a></span><br /> </p> </td></tr> <tr> <td align="center" style="width:50%; padding:5px 2%;" valign="top"> <p><span style="font-size: 120%;"><a href="/wiki/Special:AllPages" title="Special:AllPages">Pages A-Z</a></span><br /> Alphabetically ordered index of all pages </p> </td> <td align="center" style="width:50%; padding:5px 2%;" valign="top"> <p><span style="font-size: 120%;"><a href="/wiki/Special:RecentChanges" title="Special:RecentChanges">Recent Changes</a> </span><br /> List of previous changes on EOM </p> </td></tr> <tr> <td align="center" style="width:50%; padding:5px 2%;" valign="top"> <p><span style="font-size: 120%;"><a href="/wiki/Talk:EoM:This_project" title="Talk:EoM:This project"> EoM Project Talk</a></span><br /> Discuss the EoM project with others </p> </td> <td align="center" style="width:50%; padding:5px 2%;" valign="top"> <p><span style="font-size: 120%;"><a href="/wiki/Talk:EoM:This_project#Categories" title="Talk:EoM:This project"> EoM Categories</a></span><br /> How to categorize EoM pages (still under discussion) </p> </td></tr> <tr> <td align="center" style="width:50%; padding:5px 2%;" valign="top"> <p><span style="font-size: 120%;"><a href="/wiki/Help:Contents" title="Help:Contents"> Help</a></span><br /> Some hints concerning editing on EoM </p> </td> <td align="center" style="width:50%; padding:5px 2%;" valign="top"> <p><span style="font-size: 120%;"><a href="/wiki/Special:Version" title="Special:Version"> Special:Version</a></span><br /> Our installed software </p> </td></tr> </tbody></table> <p><br /> </p>    </div></div>   <div class="printfooter"> Retrieved from "<a dir="ltr" href="https://encyclopediaofmath.org/index.php?title=Main_Page&oldid=45949">https://encyclopediaofmath.org/index.php?title=Main_Page&oldid=45949</a>" </div>   <div id="catlinks" class="catlinks catlinks-allhidden" data-mw="interface"></div>  <div class="visualClear"></div>   </div>  </div> </div> </div> <div id="footer"> <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 22 May 2020, at 06:08.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="/wiki/Encyclopedia_of_Mathematics:Privacy_policy" title="Encyclopedia of Mathematics:Privacy policy">Privacy policy</a></li> <li id="footer-places-about"><a href="/wiki/Encyclopedia_of_Mathematics:About" class="mw-redirect" title="Encyclopedia of Mathematics:About">About Encyclopedia of Mathematics</a></li> <li id="footer-places-disclaimer"><a href="/wiki/Encyclopedia_of_Mathematics:General_disclaimer" title="Encyclopedia of Mathematics:General disclaimer">Disclaimers</a></li> </ul> <ul id="footer-icons"> <li><a href="/index.php/Encyclopedia_of_Mathematics:Copyrights">Copyrights</a> </li> <li> <a href="/index.php/Encyclopedia_of_Mathematics:Legal">Impressum-Legal</a></li> </ul> <div style="clear:both"></div> <span class="manage-cookies"><a class="optanon-show-settings">Manage Cookies</a></span> </div>  <script type="<br /> <b>Warning</b>: Undefined array key "jsmimetype" in <b>/var/www/html/includes/skins/QuickTemplate.php</b> on line <b>99</b><br /> "> if ( window.isMSIE55 ) fixalpha(); </script>   <script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgPageParseReport":{"limitreport":{"cputime":"0.010","walltime":"0.012","ppvisitednodes":{"value":24,"limit":1000000},"postexpandincludesize":{"value":0,"limit":2097152},"templateargumentsize":{"value":0,"limit":2097152},"expansiondepth":{"value":2,"limit":40},"expensivefunctioncount":{"value":0,"limit":100},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":0,"limit":5000000},"timingprofile":["100.00% 0.000 1 -total"]},"cachereport":{"timestamp":"20241126012441","ttl":86400,"transientcontent":false}}});mw.config.set({"wgBackendResponseTime":59});});</script></div> </div> </body> </html>