| |
This book has been designed primarily for students at the masters and doctoral levels. It 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 (monotone and dominated, as well as Fatou’s lemma). An entire chapter is devoted to complex measures, Lp spaces, Radon–Nikodym theorem and the Riesz representation theorem. The elements of probability theory (random variables, distributions, independence, product measures spaces) as also the law of large numbers and central limit theorem are presented. Discrete time Markov chains, stationary distributions and limit theorems are then discussed.
Among the highlights are alternative proofs of Riesz representation theorem and the law of large numbers. Finally, the appendix treats many basic topics such as metric spaces, topological spaces and the Stone–Weierstrass theorem. ISBN 9788173716133
|
| |
Pages : 232
|