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Gaussian Measures
Vladimir I. Bogachev, Moscow State University, Russia

Mathematical Surveys and Monographs
1998; 433 pp; hardcover
Volume: 62
ISBN-10: 0-8218-1054-5
ISBN-13: 978-0-8218-1054-5
List Price: US$116
Member Price: US$92.80
Order Code: SURV/62
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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.


Graduate students, research mathematicians, and mathematical physicists working in probability, statistics, and analysis.


"A deep and detailed treatment of an important subject."

-- American Mathematical Monthly

"The scope of topics related to Gaussian processes and measures is huge. Complemented by a list of problems in each chapter, a collection of over 800 references and a detailed section of bibliographical comments, Bogachev's book covers, in varying degrees of detail, an impressive portion of the theoretical part of this scope. It does so in a clear and precise mathematical style."

-- Mathematical Reviews

Table of Contents

  • Finite dimensional Gaussian distributions
  • Infinite dimensional Gaussian distributions
  • Radon Gaussian measures
  • Convexity of Gaussian measures
  • Sobolev classes over Gaussian measures
  • Nonlinear transformations of Gaussian measures
  • Applications
  • Locally convex spaces, operators, and measures
  • Bibliographical comments
  • References
  • Index
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