Titlebook: Probability Theory; Independence, Interc Yuan Shih Chow,Henry Teicher Textbook 19882nd edition Springer-Verlag New York Inc. 1988 Martingal

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1431-875X ury, but the first serious attempts to grapple with the logical foundations of probability seem to be Keynes (1921), von Mises (1928; 1931), and Kolmogorov (193978-1-4684-0506-4978-1-4684-0504-0Series ISSN 1431-875X Series E-ISSN 2197-4136

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Classes of Sets, Measures, and Probability Spaces,envisage a set devoid of elements, a so-called empty set, and this will be denoted by Ø. Each element of a set appears only once therein and its order of appearance within the set is irrelevant. A set whose elements are themselves sets will be called a class.

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Independence,ion of independence is the abstract counterpart of a highly intuitive and empirical notion. Independence of random variables {..}, the definition of which involves the events ofσ(..) will be shown in Section 2 to concern only the joint distribution functions.

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Integration in a Probability Space,ng to . Conceptually this is extremely simple, but a certain price is paid in terms of proofs. The alternative classical approach, while employing a less intuitive definition, achieves considerable simplicity in proofs of elementary properties.

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Distribution Functions and Characteristic Functions,ability measures determined by, the given d.f.s. Since r.v.s possessing pre- assigned d.f.s can always be defined on some probability space, the language of r.v.s and probability will be utilized in many of the proofs without further ado.

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Central Limit Theorems,tion as a limit of d.f.s of normalized sums of (classically independent) random variables. Central limit theorems also govern various classes of dependent random variables and the cases of martingales and interchangeable random variables will be considered.

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Textbook 19882nd editione from the first edition is the addition of section 9.5, dealing with the central limit theorem for martingales and more general stochastic arrays. vii Preface to the First Edition Probability theory is a branch of mathematics dealing with chance phenomena and has clearly discernible links with the

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1431-875X ipal change from the first edition is the addition of section 9.5, dealing with the central limit theorem for martingales and more general stochastic arrays. vii Preface to the First Edition Probability theory is a branch of mathematics dealing with chance phenomena and has clearly discernible links