- Series: Cambridge Series in Statistical and Probabilistic Mathematics (Book 8)
- Paperback: 366 pages
- Publisher: Cambridge University Press; 1 edition (December 10, 2001)
- Language: English
- ISBN-10: 0521002893
- ISBN-13: 978-0521002899
- Product Dimensions: 7 x 0.8 x 10 inches
- Shipping Weight: 1.8 pounds (View shipping rates and policies)
- Average Customer Review: 8 customer reviews
- Amazon Best Sellers Rank: #957,649 in Books (See Top 100 in Books)
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A User's Guide to Measure Theoretic Probability (Cambridge Series in Statistical and Probabilistic Mathematics) 1st Edition
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"Unlike technical books of a previous generation, here we have an author admitting that a reader might find the subject difficult and even offering a window on the pedagogical considerations by which he shapes his exposition. Pollard does not just explain and clarify abstractions; he really sells them to a presumably skeptical reader. Thus he bridges a gap in the literature, between elementary probability texts and advanced works that presume a secure prior knowledge of measure theory...The nice layout and occasional useful diagram further amplify the friendliness of this book." Choice
"The book ... can be recommended as an excellent source in measuring theoretic probability theory as well as a handbook for everybody who studies stochastic processes in the real world." Mathematical Reviews
Rigorous probabilistic arguments, built on the foundation of measure theory introduced seventy years ago by Kolmogorov, have invaded many fields. Many students of statistics, biostatistics, econometrics, finance, and other changing disciplines now find themselves needing to absorb theory beyond what they might have learned in the typical undergraduate, calculus-based probability course. This book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students, who were expected only to have taken an undergraduate course in real analysis or advanced calculus.
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In particular, Chapter 2 of the book contains a concise yet precise presentation of the basics of measure theory needed for understanding the probability theory. I especially like the way the author writes -- the book is written to teach. It does not merely cover the subjects, but shows by examples how you can solve similar problems, which is a very valuable merit I look for in a textbook. In other words, it doesn't just give you a fish, but teach you how to fish.
I use this book together with Chung's "A course in probability theory" and Durrett's "Probability: Theory and Examples", and find it a good complement. Chung's book and Durrett's book present the probability theory in a concise/professional manner meant for the training of probabilitists, so they show clearly what the important topics are. However, this kind of presentation/proof, understandably, omits some basics of measure theory that are supposed to be known for math/stat students. Here I find Pollard's book fill in very nicely.
Contrary to an earlier reviewer, I appreciate very much the same symbol for probability and expectation, which allows a quite natural and unified treatment of the two important concepts. It brings great clarity. Also, de Finetti's notation, once introduced, seems only natural.
The tempo of the book is at once deliberate and brisk. The author makes excellent judgment selecting the coverage. He also makes good decision on when to slow down and get dirty, and when to be brief and cover territory. The discussions in the book, combining simple explanation motivation and intuition, provides exciting road map for exploring in the first reading and for surveying in later readings.