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Bogachev</strong>, <em>Moscow State University, Russia</em></p> <p> Publication: Mathematical Surveys and Monographs<br /> Publication Year: <a href="/books/surv/year/1998">1998</a>; Volume 62<br /> ISBNs: 978-1-4704-1869-4 (print); 978-1-4704-1289-0 (online)<br /> DOI: https://doi.org/10.1090/surv/062<br />MathSciNet review: <a href = "https://mathscinet.ams.org/mathscinet-getitem?mr=1642391">MR1642391</a><br />MSC: Primary 60B11; Secondary 28C20, 46G12, 60G15, 60H07 <p><a href="https://www.copyright.com/openurl.do?isbn=978-1-4704-1289-0&WT.mc.it=American%20Mathematical%20Society" target="_blank"> <img src="/journals/images/rightslink/request-permissions.gif" /></a> </p><script type='text/javascript'> $.ajax({async: true, format: 'json', success: bkstore_link_success, error: bkstore_link_error, dataType: 'json', data: {product_code: 'SURV/62.S', check_stripped: '1'}, method: 'GET', url: '/cgi-bin/tizra/tizra_id_from_product_code', }); function bkstore_link_success(result, status, xhr) { if (result.tizra_id && result.base_product_code) { // alert(result.tizra_id); var buyBookDiv = document.getElementById('buy_in_amsbookstore_div'); var pars = buyBookDiv.getElementsByTagName('p'); var p; var customUrl = result.base_product_code.toLowerCase(); customUrl = customUrl.replace(/\/|\./g, '-'); if (pars.length > 0) { p = pars[0]; } else { p = document.createElement('p'); buyBookDiv.appendChild(p); } var s = 'Individuals and AMS Members may purchase this title '+ 'on the AMS bookstore: '+ '<a href="http://bookstore.ams.org/'+customUrl+'">'+ '<img src="/images/buttons/buy-now-a.png" /></a>'; p.innerHTML = s; } else if (result.error) { // Do nothing. This means we shouldn't display the link. // In development, we might want to display the error: if (false) alert('Error: '+result.error); } else { // do nothing? } } function bkstore_link_error(xhr, textStatus, errorThrown) { // We just do nothing if the ajax call fails. // If we want to test in development, can do something like: if (false) alert('status: '+textStatus+'\nerror: '+errorThrown); } </script> <div id='buy_in_amsbookstore_div'> </div> <p><img alt="PDF" width="15px" src="https://www.ams.org/images/ePubPDFimage.png"/> <strong><a href="surv062.pdf">View full volume as PDF</a></strong></p> <p><a id = "displayText" href="javascript:toggle();">Read more about this volume</a></p> <div id="toggleText" style="display: none"> <p>This book gives a systematic exposition of the modern theory of Gaussian measures. It presents with complete and detailed proofs fundamental facts about finite and infinite dimensional Gaussian distributions. Covered topics include linear properties, convexity, linear and nonlinear transformations, and applications to Gaussian and diffusion processes. Suitable for use as a graduate text and/or a reference work, this volume contains many examples, exercises, and an extensive bibliography. It brings together many results that have not appeared previously in book form.</p> <p><img src="/images/ver_arrow.gif" alt="" hspace="3" border="0" />Readership</p> <p>Graduate students, research mathematicians, and mathematical physicists working in probability, statistics, and analysis.</p> </div> <script src="/books/javascript/nav_all.js" type="text/javascript"></script> <form action="" method="post" name="load_alternate"> <p><strong>View other years and volumes:</strong> <script type="text/javascript"> ebook_all_years_menu("surv", "1998"); ebook_volume_menu("surv", "1998" , 62 ); </script> <input type="text" placeholder="Or type in a volume" name="volText" id="volText" /> <input type="button" name="button" id="button" value="Submit" onclick="location = load_ebook_volume('surv', document.load_alternate.volText.value);" /> </form> <h3>Table of Contents</h3> <p><img alt="PDF" width="15px" src="https://www.ams.org/images/ePubPDFimage.png"/> <strong>Download chapters as PDF</strong></p> <p><strong>Front/Back Matter</strong></p> <ul class="pdfIcon"> <li><a href="surv062-endmatter.pdf">View this volume's front and back matter</a></li> </ul> <p><strong>Chapters</strong></p> <ul class='pdfIcon'> <li>1. <a name = "01" href = "01">Finite dimensional Gaussian distributions </a> </li> <li>2. <a name = "02" href = "02">Infinite dimensional Gaussian distributions </a> </li> <li>3. <a name = "03" href = "03">Radon Gaussian measures </a> </li> <li>4. <a name = "04" href = "04">Convexity of Gaussian measures </a> </li> <li>5. <a name = "05" href = "05">Sobolev classes over Gaussian measures </a> </li> <li>6. <a name = "06" href = "06">Nonlinear transformations of Gaussian measures </a> </li> <li>7. <a name = "07" href = "07">Applications </a> </li></ul> </section> </div>  </div> </main>   <link href="/fontawesome/css/all.css" rel="stylesheet">  <link href="/css/2022-print.css" media="print" rel="stylesheet" />  <footer id="pagefooter"> <div> <a href="/"><img src="/images/content/footer-line.png" alt="Link to the American Mathematical Society homepage" class="img-responsive" loading="lazy" width="2197" height="100" aria-label="Return to homepage"></a></div> <section class="col-md-12 col-sm-12 text-center"> <aside class="row" id="">  <script src="https://kit.fontawesome.com/2ad6d7fbd6.js" crossorigin="anonymous" defer></script> <ul class="list-inline"> <li class="list-inline-item"><a href="https://www.facebook.com/amermathsoc" class="link-dark" title="Follow us on Facebook" aria-label="View the AMS on Facebook"><i class="fa-brands fa-facebook-f"></i></a></li> <li class="list-inline-item"><a href="https://twitter.com/amermathsoc" class="link-dark" title="Follow us on X" aria-label="View the AMS on X"><i class="fa-brands fa-x-twitter"></i></a></li> <li class="list-inline-item"><a href="https://www.linkedin.com/company/51001" class="link-dark" title="Follow us on LinkedIn" aria-label="View the AMS on LinkedIn"><i class="fa-brands fa-linkedin-in"></i></a></li> <li class="list-inline-item"><a href="https://www.instagram.com/amermathsoc" class="link-dark" title="Follow us on Instagram" aria-label="View the AMS on Instagram"><i class="fa-brands fa-instagram"></i></a></li> <li class="list-inline-item"><a href="https://www.youtube.com/amermathsoc" class="link-dark" title="Follow us on YouTube" aria-label="View the AMS on YouTube"><i class="fa-brands fa-youtube"></i></a></li> </ul> </aside> <p>American Mathematical Society · <a href="https://goo.gl/maps/ZvJdkQEC79p" title="Google map 201 Charles Street Providence, Rhode Island" aria-label="Google map to AMS headquarters">201 Charles Street Providence, Rhode Island 02904-2213</a> · <a href="/reach" aria-label="Contact Us">Contact Us</a></p> <p><small>AMS, American Mathematical Society, the tri-colored AMS logo, and Advancing research, Creating connections, are trademarks and services marks of the American Mathematical Society and registered in the U.S. Patent and Trademark Office.</small></p> <p> © <a href="/copyright" aria-label="Copyright policy">Copyright</a> <script> var now = new Date(); 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