Real Analysis and Probability Theory - Classic Original Book Collection (English Version. 2nd Edition) (English Version. 2nd Edition)

Author: Dudley
Publisher:
Publication Date: 2006-07-01
Features: This is a highly acclaimed textbook that clearly explains modern probability theory and the interaction between metric spaces and probability measures. The book is divided into two parts. The first part introduces the content of real analysis, including basic set theory, general topology, measure theory, integration, Banach spaces, and an introduction to functional analysis in topological spaces, convex sets and functions, and measures on topological spaces. The second part introduces the content of probability based on measure theory, including the law of large numbers, ergodic theorems, central limit theorems, conditional expectations, and martingale convergence. Additionally, the chapter on stochastic processes (Chapter 12) introduces Brownian motion and Brownian bridges. Compared to the previous edition, this edition is more comprehensive, starting with the basics of the real number system and the Stone-Weierstrass theorem on uniform approximation in functional algebra; several sections have been revised and improved, and historical notes have been expanded; many new exercises have been added, as well as hints for solutions to some exercises.