CINXE.COM

<!DOCTYPE html><html><head><title>Infinite Dimensional Analysis: A Hitchhiker's Guide - Charalambos D. Aliprantis, Kim C. Border - Google Books</title><link rel="stylesheet" href="/books/css/_4ce12830e9ca0c2644b9edacb77f7666/kl_about_this_book_kennedy_full_bundle.css" type="text/css" /><link rel="stylesheet"href="https://fonts.googleapis.com/css2?family=Product+Sans:wght@400"><script src="/books/javascript/atb_4ce12830e9ca0c2644b9edacb77f7666__en.js"></script><link rel="canonical" href="https://books.google.com/books/about/Infinite_Dimensional_Analysis.html?id=4hIq6ExH7NoC"/><meta property="og:url" content="https://books.google.com/books/about/Infinite_Dimensional_Analysis.html?id=4hIq6ExH7NoC"/><meta name="title" content="Infinite Dimensional Analysis"/><meta name="description" content="This new edition of The Hitchhiker鈥檚 Guide has bene?tted from the comments of many individuals, which have resulted in the addition of some new material, and the reorganization of some of the rest. The most obvious change is the creation of a separate Chapter 7 on convex analysis. Parts of this chapter appeared in elsewhere in the second edition, but much of it is new to the third edition. In particular, there is an expanded discussion of support points of convex sets, and a new section on subgradients of convex functions. There is much more material on the special properties of convex sets and functions in ?nite dimensional spaces. There are improvements and additions in almost every chapter. There is more new material than might seem at ?rst glance, thanks to a change in font that - duced the page count about ?ve percent. We owe a huge debt to Valentina Galvani, Daniela Puzzello, and Francesco Rusticci, who were participants in a graduate seminar at Purdue University and whose suggestions led to many improvements, especially in chapters ?ve through eight. We particularly thank Daniela Puzzello for catching uncountably many errors throughout the second edition, and simplifying the statements of several theorems and proofs. In another graduate seminar at Caltech, many improvements and corrections were suggested by Joel Grus, PJ Healy, Kevin Roust, Maggie Penn, and Bryan Rogers."/><meta property="og:title" content="Infinite Dimensional Analysis"/><meta property="og:type" content="book"/><meta property="og:site_name" content="Google Books"/><meta property="og:image" content="https://books.google.com.sg/books/content?id=4hIq6ExH7NoC&printsec=frontcover&img=1&zoom=1&edge=curl&imgtk=AFLRE71Tq5vJwP3wNV5ybWuBSraTbxUBmpIhh1UpS9bk12460t7GInbJ7nQ-EMT18uiqZtmljUunsl5lYkiKhL6KAHcgfbmDgFlOxgC0hO-bXUWsWTrnD2yw-Cg5leM0WhOEG8rtxyqK"/><link rel="image_src" href="https://books.google.com.sg/books/content?id=4hIq6ExH7NoC&printsec=frontcover&img=1&zoom=1&edge=curl&imgtk=AFLRE71Tq5vJwP3wNV5ybWuBSraTbxUBmpIhh1UpS9bk12460t7GInbJ7nQ-EMT18uiqZtmljUunsl5lYkiKhL6KAHcgfbmDgFlOxgC0hO-bXUWsWTrnD2yw-Cg5leM0WhOEG8rtxyqK"/><script></script><style>#gbar,#guser{font-size:13px;padding-top:1px !important;}#gbar{height:22px}#guser{padding-bottom:7px !important;text-align:right}.gbh,.gbd{border-top:1px solid #c9d7f1;font-size:1px}.gbh{height:0;position:absolute;top:24px;width:100%}@media all{.gb1{height:22px;margin-right:.5em;vertical-align:top}#gbar{float:left}}a.gb1,a.gb4{text-decoration:underline !important}a.gb1,a.gb4{color:#00c !important}.gbi .gb4{color:#dd8e27 !important}.gbf .gb4{color:#900 !important} #gbar { padding:.3em .6em !important;}</style></head><body class=""><div id=gbar><nobr><a target=_blank class=gb1 href="https://www.google.com.sg/search?tab=pw">Search</a> <a target=_blank class=gb1 href="https://www.google.com.sg/imghp?hl=en&tab=pi">Images</a> <a target=_blank class=gb1 href="https://maps.google.com.sg/maps?hl=en&tab=pl">Maps</a> <a target=_blank class=gb1 href="https://play.google.com/?hl=en&tab=p8">Play</a> <a target=_blank class=gb1 href="https://www.youtube.com/?tab=p1">YouTube</a> <a target=_blank class=gb1 href="https://news.google.com/?tab=pn">News</a> <a target=_blank class=gb1 href="https://mail.google.com/mail/?tab=pm">Gmail</a> <a target=_blank class=gb1 href="https://drive.google.com/?tab=po">Drive</a> <a target=_blank class=gb1 style="text-decoration:none" href="https://www.google.com.sg/intl/en/about/products?tab=ph"><u>More</u> »</a></nobr></div><div id=guser width=100%><nobr><span id=gbn class=gbi></span><span id=gbf class=gbf></span><span id=gbe></span><a target=_top id=gb_70 href="https://www.google.com/accounts/Login?service=print&continue=https://books.google.com.sg/books%3Fid%3D4hIq6ExH7NoC%26sitesec%3Dbuy%26source%3Dgbs_buy_r%26hl%3Den&hl=en&ec=GAZACg" class=gb4>Sign in</a></nobr></div><div class=gbh style=left:0></div><div class=gbh style=right:0></div><div role="alert" style="position: absolute; left: 0; right: 0;"><a href="https://books.google.com.sg/books?id=4hIq6ExH7NoC&sitesec=buy&source=gbs_buy_r&hl=en&output=html_text" title="Screen reader users: click this link for accessible mode. Accessible mode has the same essential features but works better with your reader."><img border="0" src="//www.google.com/images/cleardot.gif"alt="Screen reader users: click this link for accessible mode. Accessible mode has the same essential features but works better with your reader."></a></div><div class="kd-appbar"><h2 class="kd-appname"><a href="/books">Books</a></h2><div class="kd-buttonbar left" id="left-toolbar-buttons"><a id="appbar-view-print-sample-link" href="https://books.google.com.sg/books?id=4hIq6ExH7NoC&printsec=frontcover&source=gbs_vpt_buy"></a><a id="appbar-view-ebook-sample-link" href=""></a><a id="appbar-patents-prior-art-finder-link" href=""></a><a id="appbar-patents-discuss-this-link" href="" data-is-grant=""></a><a id="appbar-read-patent-link" href=""></a><a id="appbar-download-pdf-link" href=""></a></div><div class="kd-buttonbar right" id="right-toolbar-buttons"></div></div><div style="display: none"><ol id="ofe-gear-menu-contents" class="gbmcc"><li class="gbe gbmtc"><a class="gbmt goog-menuitem-content" id="" href="https://www.google.com/accounts/Login?service=print&continue=https://books.google.com.sg/books%3Fop%3Dlibrary&hl=en">My library</a></li><li class="gbe gbmtc"><a class="gbmt goog-menuitem-content" id="" href="http://books.google.com.sg/support/topic/4359341?hl=en-SG">Help</a></li><li class="gbe gbmtc"><a class="gbmt goog-menuitem-content" id="" href="https://books.google.com.sg/advanced_book_search">Advanced Book Search</a></li></ol></div><div id="volume-main"><div id="volume-left"><div id=menu_container ><div id="menu_scroll_wrapper"><div id="menu_scroll" role="navigation"><div id="gb-get-book-container"><a id="gb-get-book-content" href="https://books.google.com.sg/books?id=4hIq6ExH7NoC&sitesec=buy&source=gbs_vpt_buy">Get print book</a></div><p id="gb-get-book-not-available">No eBook available<p><h3 class=about_title><a name="buy_anchor"></a></h3><div id=buy class=about_content><div id=buy_v><ul style="list-style-type: none; padding-left: 0; margin: 0;"><li><a style="white-space:normal" href="http://www.springer.com/978-3-540-32696-0?utm_medium=referral&utm_source=google_books&utm_campaign=3_pier05_buy_print&utm_content=en_08082017" dir=ltr onMouseOver="this.href='http://www.springer.com/978-3-540-32696-0?utm_medium\x3dreferral\x26utm_source\x3dgoogle_books\x26utm_campaign\x3d3_pier05_buy_print\x26utm_content\x3den_08082017';return false" onMouseDown="this.href='/url?client\x3dca-print-springer-kluwer_academic\x26format\x3dgoogleprint\x26num\x3d0\x26id\x3d4hIq6ExH7NoC\x26q\x3dhttp://www.springer.com/978-3-540-32696-0%3Futm_medium%3Dreferral%26utm_source%3Dgoogle_books%26utm_campaign%3D3_pier05_buy_print%26utm_content%3Den_08082017\x26usg\x3dAOvVaw0M4lb2fWGvbl2cN-krdVM0\x26source\x3dgbs_buy_r';return true"><span dir=ltr>Springer Shop</span></a></li><li><a style="white-space:normal" href="http://www.amazon.com/gp/search?index=books&linkCode=qs&keywords=9783540326960" dir=ltr onMouseOver="this.href='http://www.amazon.com/gp/search?index\x3dbooks\x26linkCode\x3dqs\x26keywords\x3d9783540326960';return false" onMouseDown="this.href='/url?client\x3dca-print-springer-kluwer_academic\x26format\x3dgoogleprint\x26num\x3d0\x26id\x3d4hIq6ExH7NoC\x26q\x3dhttp://www.amazon.com/gp/search%3Findex%3Dbooks%26linkCode%3Dqs%26keywords%3D9783540326960\x26usg\x3dAOvVaw2gBWI8ADnsFSGFtk1ZISO5\x26source\x3dgbs_buy_r';return true"><span dir=ltr>Amazon.com</span></a></li><li><a style="white-space:normal" href="http://www.mphonline.com/books/nsearch.aspx?do=detail&pcode=9783540326960" dir=ltr onMouseOver="this.href='http://www.mphonline.com/books/nsearch.aspx?do\x3ddetail\x26pcode\x3d9783540326960';return false" onMouseDown="this.href='/url?client\x3dca-print-springer-kluwer_academic\x26format\x3dgoogleprint\x26num\x3d0\x26id\x3d4hIq6ExH7NoC\x26q\x3dhttp://www.mphonline.com/books/nsearch.aspx%3Fdo%3Ddetail%26pcode%3D9783540326960\x26usg\x3dAOvVaw3O7eThxBb467Onh_1dCX8o\x26source\x3dgbs_buy_r';return true"><span dir=ltr>MPH</span></a></li><li><a style="white-space:normal" href="https://www.popular.com.sg/catalogsearch/result/?q=9783540326960" dir=ltr onMouseOver="this.href='https://www.popular.com.sg/catalogsearch/result/?q\x3d9783540326960';return false" onMouseDown="this.href='/url?client\x3dca-print-springer-kluwer_academic\x26format\x3dgoogleprint\x26num\x3d0\x26id\x3d4hIq6ExH7NoC\x26q\x3dhttps://www.popular.com.sg/catalogsearch/result/%3Fq%3D9783540326960\x26usg\x3dAOvVaw2a_bkEG8bBclnNOjbVTj61\x26source\x3dgbs_buy_r';return true"><span dir=ltr>Popular</span></a></li><li><hr style="margin-right: 20%; color: #666;"></li><li><a style="white-space:normal" href="https://books.google.com.sg/url?id=4hIq6ExH7NoC&q=http://www.worldcat.org/oclc/1073202533&clientid=librarylink&usg=AOvVaw06IqlsEBMIg7r2LFtmgcxZ&source=gbs_buy_r"><span dir=ltr>Find in a library</span></a></li><li><a class="secondary" style="white-space:normal" href="https://books.google.com.sg/books?id=4hIq6ExH7NoC&sitesec=buy&source=gbs_buy_r" id="get-all-sellers-link"><span dir=ltr>All sellers</span> »</a></li></ul></div></div><div class=menu id=menu><div class="menu_content" style="margin-bottom:6px"><div style="margin-bottom:4px"><div class="sidebarnav"><table border="0" cellpadding="0" cellspacing="0"><tr><td><div class="sidebarcover"><a href="https://books.google.com.sg/books?id=4hIq6ExH7NoC&printsec=frontcover" ><img src="https://books.google.com.sg/books/content?id=4hIq6ExH7NoC&printsec=frontcover&img=1&zoom=5&edge=curl&imgtk=AFLRE73j1gPCs7oa9tYW7vStsplymUT997REpxQXERWotwpNDkkL6zxoHStSz_tujClCIlZ5FzM-5KEAu09dOz7VpqfYoAl9GGRY1Kzs6M9tHDb9ojtfecdtZ3_Be1aAEydVMtNw7Sde" alt="Front Cover" title="Front Cover" height=80 border=1 id=summary-frontcover ></a></div></td><td></td></tr></table></div><div style="clear:both"></div></div><div id="volume-info-sidebar"><h1 class="gb-volume-title" dir=ltr>Infinite Dimensional Analysis: A Hitchhiker's Guide</h1><span class="addmd">By Charalambos D. Aliprantis, Kim C. Border</span></div><div style="margin-bottom:3px"></div><div><p><a id="sidebar-atb-link" href="https://books.google.com.sg/books?id=4hIq6ExH7NoC&source=gbs_navlinks_s"><span dir=ltr>About this book</span></a></p></div></div></div><div class="sidebar-hr"></div><div class="ebook-promo"><a href="https://play.google.com/store/books"><img border="0" src="/googlebooks/images/ebook_promo.png" /><h3 class="section">Shop for Books on Google Play</h3><p class="ebook-promo-description">Browse the world's largest eBookstore and start reading today on the web, tablet, phone, or ereader.</p><p class="ebook-promo-clickme">Go to Google Play Now »</p></a></div><div class="sidebar-hr"></div><div><div id="navbarContainer" class="gb-navbar"></div><script>_OC_InitNavbar({"child_node":[{"title":"My library","url":"https://books.google.com.sg/books?uid=114584440181414684107\u0026source=gbs_lp_bookshelf_list","id":"my_library","collapsed":true},{"title":"My History","url":"","id":"my_history","collapsed":true}],"highlighted_node_id":""});</script><h3 class=about_title><a name="pub_info_anchor"></a></h3><div id=pub_info class=about_content><div id=pub_info_v><table cellspacing=0><tr><td><a href="https://books.google.com.sg/url?id=4hIq6ExH7NoC&q=http://www.springer.com/shop&clientid=ca-print-springer-kluwer_academic&linkid=1&usg=AOvVaw2sW989LxP0D4BcsE5OH2kl&source=gbs_pub_info_r" style="text-decoration:none"><img width=128 height=35 border=0 src="https://pagead2.googlesyndication.com/pagead/imgad?id=CO7fk9CGmazKVRC3ARgyMghnyJwCmweo7A" alt="Springer Science & Business Media"></a><tr><td style="font-size:84.6%;color:#666666">Pages displayed by permission of <a class=link_aux href="https://books.google.com.sg/url?id=4hIq6ExH7NoC&q=http://www.springer.com/shop&clientid=ca-print-springer-kluwer_academic&linkid=1&usg=AOvVaw2sW989LxP0D4BcsE5OH2kl&source=gbs_pub_info_r">Springer Science & Business Media</a>. <a style="color:#7777cc;white-space:normal" href="https://books.google.com.sg/books?id=4hIq6ExH7NoC&printsec=copyright&source=gbs_pub_info_r">Copyright</a>. </table></div></div></div></div></div></div></div><div id="volume-center"><div id="scroll_atb" role="main"><div class="vertical_module_list_row"><div id="v2_summary" class="about_content"><h1 class="summary_header">Buy this book</h1><div id="summary_content"><br> <span><a style="white-space:normal" href="https://books.google.com.sg/url?id=4hIq6ExH7NoC&q=http://www.worldcat.org/oclc/1073202533&clientid=librarylink&usg=AOvVaw06IqlsEBMIg7r2LFtmgcxZ&source=gbs_buy_section">Find in a library</a></span><br><br><table cellspacing=0><tr><th class=column>Seller</th><th class=column>Price</th><th class=column>Seller rating</th></tr><tr class="seller-row-alt"><td class=column><a href="/url?client=ca-print-springer-kluwer_academic&format=googleprint&num=0&id=4hIq6ExH7NoC&q=http://www.springer.com/978-3-540-32696-0%3Futm_medium%3Dreferral%26utm_source%3Dgoogle_books%26utm_campaign%3D3_pier05_buy_print%26utm_content%3Den_08082017&usg=AOvVaw0M4lb2fWGvbl2cN-krdVM0" dir=ltr>Springer Shop</a></td><td class=column style="text-align:right;"><span class=noprice>No price</span></td><td class=column><span class=norating>No rating</span></td></tr><tr><td class=column><a href="/url?client=ca-print-springer-kluwer_academic&format=googleprint&num=0&id=4hIq6ExH7NoC&q=http://www.amazon.com/gp/search%3Findex%3Dbooks%26linkCode%3Dqs%26keywords%3D9783540326960&usg=AOvVaw2gBWI8ADnsFSGFtk1ZISO5" dir=ltr>Amazon.com</a></td><td class=column style="text-align:right;"><span class=noprice>No price</span></td><td class=column><span class=norating>No rating</span></td></tr><tr class="seller-row-alt"><td class=column><a href="/url?client=ca-print-springer-kluwer_academic&format=googleprint&num=0&id=4hIq6ExH7NoC&q=http://www.mphonline.com/books/nsearch.aspx%3Fdo%3Ddetail%26pcode%3D9783540326960&usg=AOvVaw3O7eThxBb467Onh_1dCX8o" dir=ltr>MPH</a></td><td class=column style="text-align:right;"><span class=noprice>No price</span></td><td class=column><span class=norating>No rating</span></td></tr><tr><td class=column><a href="/url?client=ca-print-springer-kluwer_academic&format=googleprint&num=0&id=4hIq6ExH7NoC&q=https://www.popular.com.sg/catalogsearch/result/%3Fq%3D9783540326960&usg=AOvVaw2a_bkEG8bBclnNOjbVTj61" dir=ltr>Popular</a></td><td class=column style="text-align:right;"><span class=noprice>No price</span></td><td class=column><span class=norating>No rating</span></td></tr><tr class="seller-row-alt"><td class=column><a href="/url?client=ca-print-springer-kluwer_academic&format=googleprint&num=0&id=4hIq6ExH7NoC&q=https://www.amazon.sg/Infinite-Dimensional-Analysis-Hitchhikers-Guide/dp/3540326960%3Fsource%3Dps-sl-shoppingads-lpcontext%26ref_%3Dfplfs%26psc%3D1%26smid%3DA78PUD8UBC03E&usg=AOvVaw0I0QQfArKRKlIbYsLuyMnM" dir=ltr>Amazon.sg - Seller</a></td><td class=column style="text-align:right;"><span class=price>SGD聽100.39</span></td><td class=column><span class=norating>No rating</span></td></tr></table></div></div></div><script>_OC_addFlags({Host:"https://books.google.com.sg/", IsZipitFolderCollectionEnabled:1, IsBooksUnifiedLeftNavEnabled:1, IsBooksRentalEnabled:1, IsBrowsingHistoryEnabled:1});_OC_Run({"is_cobrand":false,"sign_in_url":"https://www.google.com/accounts/Login?service=print\u0026continue=https://books.google.com.sg/books%3Fid%3D4hIq6ExH7NoC%26sitesec%3Dbuy%26source%3Dgbs_buy_r%26hl%3Den\u0026hl=en"}, {"volume_id":"4hIq6ExH7NoC","is_ebook":false,"volumeresult":{"has_flowing_text":false,"has_scanned_text":true,"can_download_pdf":false,"can_download_epub":false,"is_pdf_drm_enabled":false,"is_epub_drm_enabled":false},"sample_url":"https://play.google.com/books/reader?id=4hIq6ExH7NoC\u0026source=gbs_atb_hover","is_browsable":true,"is_public_domain":false}, {});</script><div id="footer_table" style="font-size:83%;text-align:center;position:relative;top:20px;height:4.5em;margin-top:2em"><div style="margin-bottom:8px"><a href="/intl/en/googlebooks/about.html"><nobr><nobr>About Google Books</nobr></nobr></a> - <a href="/intl/en/googlebooks/privacy.html"><nobr><nobr>Privacy Policy</nobr></nobr></a> - <a href="/intl/en/googlebooks/tos.html"><nobr><nobr>Terms of Service</nobr></nobr></a> - <a href="http://books.google.com.sg/support/partner/?hl=en-SG"><nobr><nobr>Information for Publishers</nobr></nobr></a> - <a href="http://books.google.com.sg/support/answer/180577?hl=en-SG&url=https://books.google.com.sg/books?id=4hIq6ExH7NoC&sitesec=buy&source=gbs_buy_r&hl=en&v=4hIq6ExH7NoC&is=atb"><nobr><nobr>Report an issue</nobr></nobr></a> - <a href="http://books.google.com.sg/support/topic/4359341?hl=en-SG"><nobr><nobr>Help</nobr></nobr></a> - <a href="https://www.google.com.sg/"><nobr><nobr>Google Home</nobr></nobr></a></div></div></div></div></div><script>(function() {var href = window.location.href;if (href.indexOf('?') !== -1) {var parameters = href.split('?')[1].split('&');for (var i = 0; i < parameters.length; i++) {var param = parameters[i].split('=');if (param[0] == 'focus') {var elem = document.getElementById(param[1]);if (elem) {elem.focus();}}}}})();</script>