This book covers the fundamentals of measure theory and probability theory. It begins with the construction of Lebesgue measure via Caratheodory’s outer measure approach and goes on to discuss integration and standard convergence theorems and contains an entire chapter devoted to complex measures, Lp spaces, Radon–Nikodym theorem, and the Riesz representation theorem. It presents the elements of probability theory, the law of large numbers, and central limit theorem. The book then discusses discrete time Markov chains, stationary distributions and limit theorems. The appendix covers many basic topics such as metric spaces, topological spaces and the Stone–Weierstrass theorem.
- ISBN10 1439801266
- ISBN13 9781439801260
- Publish Date 11 February 2009
- Publish Status Active
- Publish Country US
- Publisher Taylor & Francis Inc
- Imprint CRC Press Inc
- Format Hardcover
- Pages 232
- Language English