A Basic Course in Measure and Probability

A Basic Course in Measure and Probability

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Vladas Pipiras Ross Leadbetter
Cambridge University Press, 1/30/2014
EAN 9781107020405, ISBN10: 1107020409

Hardcover, 376 pages, 23.1 x 15.5 x 2.3 cm
Language: English

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.

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