Integration and probability
By: Paul Malliavin, in cooperation with Hélène Airault, Leslie Kay, Gérard Letac.
Contributors: Letac, Gérard.
Series: Graduate texts in mathematics ;; 157
Publisher: Springer-Verlag
Published: 1995
Place of publication: New York
Language: eng
Number of pages: 322
Subjects: Calculus, Integral; Spectral theory (Mathematics); Fourier analysis
Description: 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.
Notes: Accompanied by: Exercises and solutions manual for Integration and probability / Gérard Letac. viii, 142 p. ; 24 cm.
Includes index.