Limit Distributions for Sums of Independent Random Variables

asymptotically constant B. V. Gnedenko Borel sets bounded variation c₁ characteristic function continuity points converge defined definition dF(x dFnk x distribution function F(x distribution laws domain of attraction domain of partial elementary events equation exists fn(t Fn(x follows Hence identically distributed independent random variables inequality infinitely divisible law infinitesimal integral interval large numbers lattice distribution law F(x law of large Lebesgue integral lim lim limit distribution function limit law limit theorems log f(t mathematical expectation measure necessary and sufficient normal distribution normal law obtain partial attraction Poisson law Proof proved satisfied sequence stable law sufficiently large suitably chosen constants summands sums of independent theory of probability tion Translator's note unimodal unimodal distribution values weak convergence x² dFnk xdF(x xdFnk ζη ξη ξι