Measure Theory and Probability Theory

by Krishna B. Athreya, Soumendra N. Lahiri

This is a graduate level textbook on measure theory and probability theory. It presents the main concepts and results in measure theory and probability theory in a simple and easy-to-understand way. It further provides heuristic explanations behind the theory to help students see the big picture. The book can be used as a text for a two semester sequence of courses in measure theory and probability theory, with an option to include supplemental material on stochastic processes and special topics. Prerequisites are kept to the minimal level and the book is intended primarily for first year Ph.D. students in mathematics and statistics.

Genres: Mathematics

637 pages, Hardcover

First published July 1, 2006

Reviews

[Adam · Rating 4 out of 5]

I can't say that I love its thin coverage of Measure Theory. But on the other hand, other books which try to do both Measure and Probability Theory have similarly thin coverage of each. Of course one can just learn Measure Theory, but then jumping to a book on Probability Theory usually is a rough process of switching to different names of theorems, definitions of objects, and so on. Especially because books dedicated to just Probably Theory often don't strive for the same level of thoroughness that books on foundational mathematics like Measure Theory do -- so the style, interests, methods, of pure Probability Theory textbooks are not usually to my taste either.

So the book is good, but I think the authors see their true objective as getting to the Probability Theory so that the reader can be equipped to do research or further studies. I would like to have a textbook that regards all the ideas and steps along the way as more worthy of detailed investigation.