A Basic Course in Measure and Probability
Theory for Applications

A concise introduction covering all of the measure theory and probability most useful for statisticians.

Ross Leadbetter (Author), Stamatis Cambanis (Author), Vladas Pipiras (Author)

9781107652521, Cambridge University Press

Paperback / softback, published 30 January 2014

374 pages, 15 b/w illus. 300 exercises
22.8 x 15.1 x 1.6 cm, 0.6 kg

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.

Preface
Acknowledgements
1. Point sets and certain classes of sets
2. Measures: general properties and extension
3. Measurable functions and transformations
4. The integral
5. Absolute continuity and related topics
6. Convergence of measurable functions, Lp-spaces
7. Product spaces
8. Integrating complex functions, Fourier theory and related topics
9. Foundations of probability
10. Independence
11. Convergence and related topics
12. Characteristic functions and central limit theorems
13. Conditioning
14. Martingales
15. Basic structure of stochastic processes
References
Index.

Subject Areas: Stochastics [PBWL], Probability & statistics [PBT], Calculus & mathematical analysis [PBK]