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Integration and Probability (Graduate Texts in Mathematics) (v. 157)

Posted on 2010-03-16




Name:Integration and Probability (Graduate Texts in Mathematics) (v. 157)
ASIN/ISBN:0387944095
Language:English
File size:6.6 Mb
Language: English
Publish Date: 1995-06-13
ISBN: 0387944095
Pages: 322 pages
File Type: PDF
File Size: 6,6 MB
Other Info: Springer
   Integration and Probability (Graduate Texts in Mathematics) (v. 157)

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Paul Malliavin ""

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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