Real Analysis and Probability
2nd Revised edition
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Real Analysis and Probability by R. M. Dudley
Book DescriptionThis classic textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The first half of the book gives an exposition of real analysis: basic set theory, general topology, measure theory, integration, an introduction to functional analysis in Banach and Hilbert spaces, convex sets and functions and measure on topological spaces. The second half introduces probability based on measure theory, including laws of large numbers, ergodic theorems, the central limit theorem, conditional expectations and martingale's convergence. A chapter on stochastic processes introduces Brownian motion and the Brownian bridge. The edition has been made even more self-contained than before; it now includes a foundation of the real number system and the Stone-Weierstrass theorem on uniform approximation in algebras of functions. Several other sections have been revised and improved, and the comprehensive historical notes have been further amplified. A number of new exercises have been added, together with hints for solution.
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Book DetailsISBN: 9780521809726
(228mm x 152mm x 35mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 14-Oct-2002
Country of Publication: United Kingdom
Books By Author R. M. Dudley
Uniform Central Limit Theorems, Paperback (February 2014)
This expanded edition of the classic work on empirical processes now boasts several new proved theorems not in the first.
Real Analysis and Probability, Paperback (October 2002)» View all books by R. M. Dudley
This classic text offers a clear exposition of modern probability theory.
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