Exercises and Solutions Manual for Integration and Probability

Download or read book Exercises and Solutions Manual for Integration and Probability written by Paul Malliavin and published by Springer Science & Business Media. This book was released on 1995-06-13 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.