Probability and Measure Theory

Probability and Measure Theory, Second Edition, is a text for a graduate-level course in probability that includes essential background topics in analysis. It provides extensive coverage of conditional probability and expectation, strong laws of large numbers, martingale theory, the central limit theorem, ergodic theory, and Brownian motion.

Clear, readable styleSolutions to many problems presented in textSolutions manual for instructorsMaterial new to the second edition on ergodic theory, Brownian motion, and convergence theorems used in statisticsNo knowledge of general topology required, just basic analysis and metric spacesEfficient organization

Summary of Notation
Fundamentals of Measure and Integration Theory
Further Results in Measure and Integration Theory
Introduction to Functional Analysis
Basic Concepts of Probability
Conditional Probability and Expectation
Strong Laws of Large Numbers and Martingale Theory
The Central Limit Theorem
Ergodic Theory
Brownian Motion and Stochastic Integrals