Real Analysis And Probability 2nd Edition R M Dudley by R. M. Dudley 9780521809726, 052180972X instant download after payment.

This much admired textbook, now reissued in paperback, 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 convergence.
A chapter on stochastic processes introduces Brownian motion and the
Brownian bridge.
The new edition has been made even more self-contained than before;
it now includes early in the book 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 extensive historical notes have been further amplified. A number of new
exercises, and hints for solution of old and new ones, have been added.
R. M. Dudley is Professor of Mathematics at the Massachusetts Institute of
Technology in Cambridge, Massachusetts.