## Limit distributions for sums of independent random variables |

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### Contents

PREFACE | 1 |

Probability Distributions Random Variables | 13 |

Distributions in Rl and Their Characteristic Functions | 32 |

Copyright | |

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arbitrary asymptotically constant B. V. Gnedenko belongs Borel Borel sets bounded variation central limit theorem characteristic function constants Bn continuity points converge deduce defined definition denote dF'nj dF'nj(y dFnk dFnk(x dG(y distribution function F(x distribution laws domain of attraction domain of partial elementary events equation example exists finite variance Fn(x follows Hence identically distributed independent random variables inequality infinitely divisible distribution infinitely divisible law infinitesimal interval large numbers lattice distribution law F(x law of large Lebesgue integral Lemma limit distribution function limit law limit theorems mathematical expectation measure necessary and sufficient normal distribution normal law obtained partial attraction Poisson law preceding theorem probability density probability distribution problem Proof properties proved satisfied sequence stable law Stieltjes integral sufficiently large suitably chosen constants sums of independent suppose theory of probability Translator's note uniformly with respect unimodal unimodal distribution weak convergence zero