Measure theory / J.L. Doob

This is a textbook on measure theory written by a probabilist for the probabilists. The concepts are motivated by non-mathematical models such as coin-tossing (p. 28) and card-mixing (p. 80). The book is self- contained and expertly presented. The special features include the use of pseudometric spaces (instead of metric spaces), results pertaining to probability theory (such as martingale theory). Otherwise the contents are standard and classical, for example, the Radon-Nikodým theorem and the Vitali-Hahn-Saks theorem. It has a special chapter on measures on the real line. Also, a series of applications is briefly introduced at the end of the book.

The author has other readers in mind as a.e. (almost everywhere) is used throughout the book until the last chapter where a.s. (almost surely) is used. Though it is a book for the probabilists to learn analysis, it is also a book for the analysts to orientate themselves towards probability. In this way, the book is unique. (Zentralblatt)

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