A First Look at Rigorous Probability Theory

Rating:
Summary: Excellent primer to use as supplement or for review
Review: This is a marvelous primer on measure-theoretic probability. I came across it a couple of years after taking a course based on Chung's famous text ("A Course in Prob. Theory") and found it to be an excellent book for review and remediation--that is, it helped me get a better overview of the material I had already learned and it helped me learn topics such as, say, uniform integrability, that didn't sink in too well the first time around.

According to the preface, the author prepared most of the book as supplemental class notes for the benefit of his students in a course whose main text was, if I recall correctly, Billingsley's excellent "Probability and Measure". The students were so enthusiastic about the usefulness of Professor Rosenthal's supplemental info that they insisted he publish it, despite his objection that the book wasn't original enough to warrant entry into an already crowded field. Well, the students made the right call: Rosenthal's clear and concise text will, I think, help almost any student learn measure-theoretic probability more efficiently. I'd also recommend it to folks who need a concise review of measure-theoretic probability.