Probability and Measure

First thing, this book isn't not appropriate for undergrads, therefore if you are an undergrad, please look for a suitable book for your level and don't post reviews that may mislead other customers. It is also not appropriate for business majors or fields that deal exclusively with applied statistics and probability. If you are a graduate student in mathematics, statistics or economics (with concentration in econometrics), if you need theoretical probability, this is a must have book. The proofs are presented in a very solid way. Some are even beautiful masterpieces. The same can be said to some motivation for particular issues, for instance, using diatic expansion to motivate the whole probability theory in the first few sections. There aren't many typos, I personally haven't come across any yet. Shiryaev's Probability book is also very good; however, there are apparently more typos and in my personal opinion the explanations in Billingslley's book are a bit better. If you think good things come in two's I would suggest you also take a look at a solid, concise and cheap book, Probability Essentials by Jacod and Protter. Enjoy!!!

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.

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.

The only book on probability in graduate or senior undergraduate level that is readable. Sounds strange? Not really, probabilists in general do not know how to write readable books and examples are abundant. This book is exception. However this is not a definitive book, once you are done with it, you have to go further to learn more.

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.