Modern probability theory: an introductory textbook
A comprehensive treatment, unique in covering probability theory independently of modern theory. New edition features additional problems, examples that show scope and limitations of various results, and enlarged chapters on laws of large numbers, extensions, and generalizations.
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Sets and Classes of Events
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a-additive a-field induced arbitrary binomial Borel field Borel function Borel sets bounded called ch.fn Chapter closed under finite COMPLEMENTS AND PROBLEMS continuous convergence in probability convergence theorem converges a.s. Corollary defined definition denoted dF(x disjoint distribution function equivalent Example exists field containing finite number given Hence implies independent r.v.'s indicator function inequality infinite integrable interval inverse large numbers law of large Lebesgue measure Lemma limit martingale matrix measurable function minimal a-field containing minimal field monotone monotone convergence theorem mutually independent non-decreasing non-negative obtain outcomes P[Xn partition points Poisson probability density function probability distribution probability measure probability space Proof properties prove random variable rectangles sequence of independent sequence of r.v.'s set function Show Similarly simple function subsets Suppose takes the values transition probabilities uniformly uniquely vector