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.
General
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