- Hardcover: 608 pages
- Publisher: Wiley-Interscience; 3 edition (May 1, 1995)
- Language: English
- ISBN-10: 0471007102
- ISBN-13: 978-0471007104
- Product Dimensions: 6.4 x 1.3 x 9.6 inches
- Shipping Weight: 2.1 pounds
- Average Customer Review: 16 customer reviews
- Amazon Best Sellers Rank: #95,168 in Books (See Top 100 in Books)
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Probability and Measure 3rd Edition
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From the Back Cover
PROBABILITY AND MEASURE
Now in its new third edition, Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Retaining the unique approach of the previous editions, this text interweaves material on probability and measure, so that probability problems generate an interest in measure theory and measure theory is then developed and applied to probability. Probability and Measure provides thorough coverage of probability, measure, integration, random variables and expected values, convergence of distributions, derivatives and conditional probability, and stochastic processes. The Third Edition features an improved treatment of Brownian motion and the replacement of queuing theory with ergodic theory.
Like the previous editions, this new edition will be well received by students of mathematics, statistics, economics, and a wide variety of disciplines that require a solid understanding of probability theory.
About the Author
PATRICK BILLINGSLEY is Professor of Statistics and Mathematics at the University of Chicago. He is the coauthor (with Watson et al.) of Statistics for Management and Economics; (with D. L. Huntsberger) of Elements of Statistical Inference; and the author of Convergence of Probability Measures (Wiley-Interscience), among other works. Dr. Billingsley has also edited the Annals of Probability for the Institute of Mathematical Statistics. He received his PhD in mathematics from Princeton University.
Top customer reviews
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logical structuring of the material. I do not believe that this is a good book to learn
probability and measure theory from. If you are not already familiar with most of the concepts
then I recommend starting your journey elsewhere.
As a graduate student I very much appreciated the rigor and detailed approach in this textbook. Some of the topics like independence and martingales are developed with a rigor and details usually missing from undergraduate textbooks. If you do not like books missing any deductions this is your textbook.
But there are problems with the text, the major one being the outline and order of the exposition, sometimes it looks as if it was done at random though even that has been done with intention to facilitate understanding but has somehow gone a bit astray. For example it takes hundreds of pages to get into fairly elementary notions and then they are treated counterintuitive leaving reader without intuitive understanding of the topics. See for example exposition of expectation (general case) that is way too slow after hundreds of pages. Or discrete Markov Chains treatment early enough but completely technical and counterintuitive without ever leading a student to any concrete ideas. The integration topics are sprinkled all over the place as well.
Still I would think this is the text for introductory study of probability only with a instructor furnishing better choice and order of topics than the one presented in the textbook. It surely is one of the most detailed approaches geared toward a serious study. On the level of sofistication it does not come anywhere close to Kallenberg's "Foundations of Modern Probability" or Borovkov's "Probability Theory" but it does provide a treatise with important examples, without omissions (sometimes on the expense of elegance but every time for the benefit of reader), and with a rigor required while still being accessible to a beginning graduate student and thus it provides the important benefits of learning.
This is one of the plausible choices for two semester course in introductory graduate probability with perhaps Kai Lai Chung's classic Stanford textbook as the alternative.