A Basic Course in Measure and Probability: Theory for Applications

by Ross Leadbetter, Stamatis Cambanis, Vladas Pipiras

Originating from the authors' own graduate course at the University of North Carolina, this material has been thoroughly tried and tested over many years, making the book perfect for a two-term course or for self-study. It provides a concise introduction that covers all of the measure theory and probability most useful for statisticians, including Lebesgue integration, limit theorems in probability, martingales, and some theory of stochastic processes. Readers can test their understanding of the material through the 300 exercises provided. The book is especially useful for graduate students in statistics and related fields of application (biostatistics, econometrics, finance, meteorology, machine learning, and so on) who want to shore up their mathematical foundation. The authors establish common ground for students of varied interests which will serve as a firm 'take-off point' for them as they specialize in areas that exploit mathematical machinery.

376 pages, Hardcover

First published February 28, 2014

Reviews

[Noshgul · Rating 5 out of 5]

As any reader of this review will probably know there are loads of measure and probability books floating around. Every professor (and graduate student) seems to have his own favorite. After trying a few other books for self-study I found this one and stuck with it. It treats measure theory from a classical/non-topological point of view. The proofs are quite easy to read (as in someone with a BSc in math will find this a "quick" read, it's imo not as dense as usual graduate books). The exercises consist of the standard 1/3 basic things that you can readily solve if you've got a grasp of the defintions, 1/3 that require some more thought and 1/3 that are relatively hard. All in all it's imo a great addition to the already extensive number of books in prob and measure theory