A course in probability theory
Since the publication of the first edition of this classic textbook over thirty years ago, tens of thousands of students have used A Course in Probability Theory. New in this edition is an introduction to measure theory that expands the market, as this treatment is more consistent with current courses. While there are several books on probability, Chung's book is considered a classic, original work in probability theory due to its elite level of sophistication.
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Random variable Expectation Independence
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apply arbitrary assertion belongs Borel field Borel measurable Borel measurable function bounded called central limit theorem Chapter Chebyshev's inequality condition consequently consider constant convergence theorem converges a.e. converges in dist converges vaguely corresponding countable set defined definition denote dF(x discrete disjoint equation equivalent example exists finite number given Hence hint hypothesis identically distributed r.v.'s implies independent r.v.'s inequality infinitely divisible interval large numbers law of large left member lemma Let Xn lim sup Markov process Markov property martingale measurable function notation null set obtain oo a.e. optional r.v. permutable probability space probability theory proof of Theorem Prove random walk real numbers replaced result right member satisfying sequence of independent sequence of r.v.'s stochastic processes strictly positive submartingale subset supermartingale Suppose term trivial uniformly integrable vague convergence zero