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Integration and Probability / Edition 1

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Overview

This book is designed to be an introduction to analysis with the proper mix of abstract theories and concrete problems. It starts with general measure theory, treats Borel and Radon measures (with particular attention paid to Lebesgue measure) and introduces the reader to Fourier analysis in Euclidean spaces with a treatment of Sobolev spaces, distributions, and the Fourier analysis of such. It continues with a Hilbertian treatment of the basic laws of probability including Doob's martingale convergence theorem and finishes with Malliavin's "stochastic calculus of variations" developed in the context of Gaussian measure spaces. This invaluable contribution to the existing literature gives the reader a taste of the fact that analysis is not a collection of independent theories but can be treated as a whole.
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Editorial Reviews

From the Publisher
"If I were asked to recommend texts to research students who need a grounding in integration theory this book would be on the list...The book is excellent" - C. Barnett, Imperial College of Science, Technology and Medicine, London
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Product Details

  • ISBN-13: 9780387944098
  • Publisher: Springer New York
  • Publication date: 6/13/1995
  • Series: Graduate Texts in Mathematics Series , #157
  • Edition description: 1995
  • Edition number: 1
  • Pages: 325
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.88 (d)

Table of Contents

I Measurable Spaces and Integrable Functions 1
II Borel Measures and Radon Measures 17
III Fourier Analysis 49
IV Hilbert Space Methods and Limit Theorems in Probability Theory 79
V Gaussian Sobolev Spaces and Stochastic Calculus of Variations 133
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