Probability and Measure Theory, 2/e (Hardcover)

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 style
• Solutions to many problems presented in text
• Solutions manual for instructors
• Material new to the second edition on ergodic theory, Brownian motion, and convergence theorems used in statistics
• No knowledge of general topology required, just basic analysis and metric spaces
• Efficient organization

Robert B. Ash as written about, taught, or studied virtually every area of mathematics. His books include Information Theory, Topics in Stochastic Processes, The Calculus Tutoring Book, Introduction to Discrete Mathematics, and A Primer of Mathematics.

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.