Probability & Measure Theory


  • Robert Ash, University of Illinois, Urbana-Champaign, U.S.A.
  • Catherine Doleans-Dade, University of Illinois, Urbana-Champaign, U.S.A.

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.
View full description


Graduate students, faculty, and other professionals in mathematics, statistics, engineering, and economics; also, graduate students and professionals in physics and computer science.


Book information

  • Published: December 1999
  • ISBN: 978-0-12-065202-0


Published Reviews As reviewed at "There are numerous probability texts on the market, which makes choosing one difficult. If you are a financial professional who knows basic probability theory, but wants to take the next step in sophistication, this is the essential text. It introduces basic measure theory and functional analysis, and then delves into probability. The writing is clear and highly accessible. The choice of topics is perfect for financial engineers or financial risk managers: martingales, the inversion theorem, the central limit theorem, Brownian motion and stochastic integrals. I can't praise this book enough. It is exceptional!"

Table of Contents

Summary of NotationFundamentals 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.