Probability & Measure Theory / Edition 2

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Overview

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

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

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Editorial Reviews

From the Publisher
Published Reviews

As reviewed at http://www.contingencyanalysis.com
"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!"

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Product Details

  • ISBN-13: 9780120652020
  • Publisher: Elsevier Science
  • Publication date: 12/20/1999
  • Edition description: REV
  • Edition number: 2
  • Pages: 516
  • Sales rank: 1,004,360
  • Product dimensions: 1.31 (w) x 6.00 (h) x 9.00 (d)

Meet the Author

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.

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Table of Contents

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.

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Sort by: Showing all of 2 Customer Reviews
  • Anonymous

    Posted October 18, 2001

    one of the best, if not the best

    I couldn't agree more with the first reviewer. Anyone serious about analysis and probability theory will want to have this book handy. The book has been extremely useful in my research. Seems easy to learn from as well (although I can't speak as a student anymore). Highly recommended.

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  • Anonymous

    Posted August 3, 2000

    Probably the best text at this level on this subject

    This is an outstanding textbook suitable for a beginning graduate course in rigorous measure theoretic probability. All the essential topics are covered thoroughly. The book is beautifully and clearly written, both at the macro level in terms of the overall structure and choice of topics, and at the micro level in the presentation of individual definitions, statements of theorems and proofs. The end of section exercises are excellent, with well-written solutions to the more challenging ones given in the appendix. In my opinion competing texts either omit some (sometimes a lot) of the essential topics, or are not as well written.

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