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On a local theorem. (Russian) Zbl 0697.60030
Let $$\xi_ 1,...,\xi_ n$$ be i.i.d. random variables having mean 0 and unit variance. Denote $P_ n(x,h)=P(x\leq \xi_ 1+...+\xi_ n<x+h).$ In the case when $$\xi_ 1$$ has a non-lattice distribution, conditions are given in terms of $$P_ 1(x,h)$$ under which there exist $$x_ n$$ such that for $$x>x_ n$$ and any fixed $$h>0$$ $P_ n(x,h)=nP_ 1(x,h)(1+o(1))\quad as\quad n\to \infty.$ This is a local version of A. V. Nagaev’s theorem in Teor. Veroyatn. Primen. 22, 335-346 (1977; Zbl 0376.60055); English translation in Theory Probab. Appl. 22(1977), 326-338 (1978).
Reviewer: T.Shervashidze
##### MSC:
 60F05 Central limit and other weak theorems
##### Keywords:
local version of A. V. Nagaev’s theorem