Product Description

PROBABILITY AND MEASURE

Third Edition

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.

Product Details

• Amazon Sales Rank: #157193 in Books
• Published on: 1995-04-17
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 608 pages

From the Back Cover
PROBABILITY AND MEASURE

Third Edition

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.

Customer Reviews

Excellent introduction and reference.
This book is a thorough introduction and excellent reference book for the ideas involving probability as a measure. I would recommend this book to anyone who needs a deep understanding of probability, expectation, integration, random variables, and so forth. Good also as a graduate level or other measure-theoretic probability course. Two years after I learned these ideas, I still refer often to the text.

An exceptionally good book
I've read portions of almost every measure theoretic probability theory book published. And I've come back to Billingsley. This is a hard book to read through and through if you are a novice; this is not Billingsley's fault - it is just that the subject is hard on first acquaintance.
Billinglsey develops everything from first principles, so if you have the intellectual gumption you ought to be able to read the main text with a knowledge of plain college algebra and a little epsilon-delta practice of the sort that comes from an undergraduate real analysis course. The small print asides are fascinating but they are often addressed to a card carrying mathematician. The November 2003 reviewer who complained that Billingsley uses expectation before defining the integral fails to notice - or at any rate, to point out - that he defines only the expectation of simple random variables in the first chapter, so what is involved is just a sum, not an integral. I could sing my praises on and on. But here is the kernel of this review in a line: this is one of the best books ever written on measure theoretic probability. Full stop.

The book on probability
This book is not for everybody. It is for the professional mathematician (or physicist, or alike). All concepts are very well explained, and Billigsley does go down to the core of everything. It is, as far as I'm concerned, among the best books in math ever written, with favorites such as Feynman's lectures and Herstein's algebra manual. If you are a mathematician and want to have the top reference in probability, this is it.