An Introduction to Probability Theory and Its Applications, Volume 2Wiley, 1950 - Probabilities Vol. 2 has series: Wiley series in probability and mathematical statistics. Bibliographical footnotes. "Some books on cagnate subjects": v. 2, p. 615-616. |
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Page 104
... on the notion of continuity but not on other properties of Cartesian spaces . It is therefore applicable to arbitrary topological spaces . of either a or b are replaced by ± ∞ 104 IV.2 PROBABILITY MEASURES AND SPACES Baire Functions.
... on the notion of continuity but not on other properties of Cartesian spaces . It is therefore applicable to arbitrary topological spaces . of either a or b are replaced by ± ∞ 104 IV.2 PROBABILITY MEASURES AND SPACES Baire Functions.
Page 108
... Baire functions , and the extension is unique . When it comes to unbounded functions divergent integrals are unavoid- able , but at least for positive Baire functions it is possible to define E ( u ) either as a number or as the symbol ...
... Baire functions , and the extension is unique . When it comes to unbounded functions divergent integrals are unavoid- able , but at least for positive Baire functions it is possible to define E ( u ) either as a number or as the symbol ...
Page 125
... functions , respectively , and restrict our attention to sets and functions that can be derived from them by elementary operations and ( possibly infinitely many ) passages to the limit . This delimits the classes of Borel sets and Baire ...
... functions , respectively , and restrict our attention to sets and functions that can be derived from them by elementary operations and ( possibly infinitely many ) passages to the limit . This delimits the classes of Borel sets and Baire ...
Contents
CHAPTER | 1 |
SPECIAL DENSITIES RANDOMIZATION | 44 |
PROBABILITY MEASURES AND SPACES | 101 |
Copyright | |
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An Introduction to Probability Theory and Its Applications, Volume 2 William Feller Limited preview - 1991 |
Common terms and phrases
a₁ applies arbitrary argument assume asymptotic atoms backward equation Baire functions Borel sets bounded central limit theorem characteristic function common distribution compound Poisson condition consider constant continuous function convergence convolution defined definition denote density derived distribution F distribution function equals example exists exponential distribution F{dx finite interval fixed follows formula given hence implies independent random variables inequality infinitely divisible integral integrand Laplace transform law of large left side lemma Let F limit distribution Markov martingale measure mutually independent normal distribution notation o-algebra obvious operator parameter Poisson process positive probabilistic probability distribution problem proof prove random walk renewal epochs renewal equation renewal process S₁ sample space satisfies semi-group sequence shows solution stable distributions stochastic stochastic kernel symmetric T₁ tends theory transition probabilities uniformly unique variance vector X₁ Y₁ zero expectation