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Catalogue Information
Field name	Details
Dewey Class	519.2
Title	Gaussian Measures in Finite and Infinite Dimensions (EBook /) / by Daniel W. Stroock.
Author	Stroock, Daniel W.
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2023.
Publication	Cham : : Springer International Publishing : : Imprint: Springer, , 2023.
Physical Details	XII, 144 p. 1 illus. : online resource.
Series	Universitext 2191-6675
ISBN	9783031231223
Summary Note	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 of Gaussian measures on infinite dimensional spaces, particular attention is given to those 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. The contents of this book should be accessible to either undergraduate or graduate 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.:
Contents note	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.
Mode of acces to digital resource	Digital reproduction.-
	Cham :
	Springer International Publishing,
	2023. -
	Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	https://doi.org/10.1007/978-3-031-23122-3
Links to Related Works	Subject References: Analysis . Geometry . Mathematical analysis . Probabilities . Probability Theory . Authors: author . Stroock, Daniel W. . Corporate Authors: SpringerLink (Online service) . Series: Universitext . Classification: 519.2 .

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Gaussian Measures in Finite and Infinite Dimensions

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