Limit Distributions for Sums of Independent Random Variables |
Contents
INTRODUCTION | 13 |
The Lebesgue integral | 19 |
Probability distributions in R¹ and in | 25 |
Copyright | |
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a₁ B. V. Gnedenko B₂ Borel sets bounded variation c₁ c₂ characteristic function continuity points converge defined dFni dFnj dFnj(y dFnk x dFnx dG(y distribution function F(x distribution laws domain of attraction elementary events equation fn(t Fn(x follows Gnedenko Hence identically distributed independent random variables inequality infinitely divisible law infinitesimal integral interval large numbers law F(x law of large Lebesgue integral LEMMA lim lim limit law limit theorems log ƒ mathematical expectation measure necessary and sufficient nondecreasing normal distribution normal law partial attraction Poisson law Proof proved satisfied sequence stable law sufficiently large summands sums of independent theory of probability tion Translator's note unimodal unimodal distribution values variables Enk weak convergence x+Mnk x² dF x² dFnk