Measure Theory (Graduate Texts in Mathematics)

Rating:
Summary: Measure Theory
Review: This book will be useful to anyone who will be working in probability and is already acquainted with measure theory. It includes results that are not standard material for a real analysis text but that are of interest in probability. The author, who needs no introduction, uses simple examples (coin tossing, card shuffling) to illustrate how the "interesting, but imprecise real world" is represented in the "duller but more precise mathematical world", as well as the importance of keeping them apart. I know of no other publication where this is done as effectively and as beautifully as it is presented here. Each proof in this book is actually a sketch of its proof. This means that the reader does not get lost in details and sees the concepts transparently. The author also does a good job of limiting himself to what belongs to the title, as opposed to developing what would belong in a probability text.

I recommend this book to anyone interested in measure theory, whether or not their interest extends to probability.