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

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9780387944098: Integration and Probability (Graduate Texts in Mathematics) (v. 157)

An introduction to analysis with the right mix of abstract theories and concrete problems. Starting with general measure theory, the book goes on to treat Borel and Radon measures and introduces the reader to Fourier analysis in Euclidean spaces with a treatment of Sobolev spaces, distributions, and the corresponding Fourier analysis. 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 gives 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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Text: English (translation)
Original Language: French

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"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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Malliavin, Paul; Kay, L. [Translator]; Kay, L. [Assistant]; Airault, H. [Assistant]; Letac, G. [Assistant];
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Book Description Springer-Verlag New York Inc., United States, 1995. Hardback. Book Condition: New. 1995 ed.. Language: English . Brand New Book ***** Print on Demand *****. An introduction to analysis with the right mix of abstract theories and concrete problems. Starting with general measure theory, the book goes on to treat Borel and Radon measures and introduces the reader to Fourier analysis in Euclidean spaces with a treatment of Sobolev spaces, distributions, and the corresponding Fourier analysis. 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 gives a taste of the fact that analysis is not a collection of independent theories, but can be treated as a whole. Bookseller Inventory # APC9780387944098

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