Preface.- 1. Characteristic Functions.- 2. Gaussian Measures and Families.- 3. Gaussian Measures on a Banach Space.- 4. Further Properties and Examples of Abstract Wiener Spaces.- References.- Index.

Daniel W. Stroock is Emeritus professor of mathematics at MIT. He is a respected mathematician in the areas of analysis, probability theory and stochastic processes. Prof. Stroock has had an active career in both the research and education.   From 2002 until 2006, he was the first holder of the second Simons Professorship of Mathematics.  In addition, he has held several administrative posts, some within the university and others outside.  In 1996, the AMS awarded him together with his former colleague jointly S.R.S. Varadhan the Leroy P. Steele Prize for seminal contributions to research in stochastic processes. Finally, he is a member of both the American Academy of Arts and Sciences, the National Academy of Sciences and a foreign member of the Polish Academy of Arts and Sciences.

This text provides a concise introduction, suitable for a one-semester special topics

course, to the remarkable properties of Gaussian measures on both finite and infinite

dimensional spaces. It begins with a brief resumé of probabilistic results in which Fourier

analysis plays an essential role, and those results are then applied to derive a few basic

facts about Gaussian measures on finite dimensional spaces. In anticipation of the analysis

properties of Gaussian measures that are dimension independent, and Gaussian processes

are constructed. The rest of the book is devoted to the study of Gaussian measures on

Banach spaces. The perspective adopted is the one introduced by I. Segal and developed

by L. Gross in which the Hilbert structure underlying the measure is emphasized.

students who are interested in probability theory and have a solid background in Lebesgue

integration theory and a familiarity with basic functional analysis. Although the focus is

on Gaussian measures, the book introduces its readers to techniques and ideas that have

applications in other contexts.