Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 2, pp. 225-245
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T. V. Arak. On the rate of convergence in Kolmogorov's uniform limit theorem. I. Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 2, pp. 225-245. http://geodesic.mathdoc.fr/item/TVP_1981_26_2_a0/
@article{TVP_1981_26_2_a0,
author = {T. V. Arak},
title = {On the rate of convergence in {Kolmogorov's} uniform limit {theorem.~I}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {225--245},
year = {1981},
volume = {26},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1981_26_2_a0/}
}
TY - JOUR
AU - T. V. Arak
TI - On the rate of convergence in Kolmogorov's uniform limit theorem. I
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1981
SP - 225
EP - 245
VL - 26
IS - 2
UR - http://geodesic.mathdoc.fr/item/TVP_1981_26_2_a0/
LA - ru
ID - TVP_1981_26_2_a0
ER -
%0 Journal Article
%A T. V. Arak
%T On the rate of convergence in Kolmogorov's uniform limit theorem. I
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1981
%P 225-245
%V 26
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1981_26_2_a0/
%G ru
%F TVP_1981_26_2_a0
Theorem. {\it For any probability distribution function $F$ on $R$ and for any natural number $n$ there exists an infinitely divisible distribution function $B$ such that $$ \sup_x|F^{n*}(x)-B(x)|\le C_n^{-2/3} $$ } Here $F^{n*}$ is the $n$-fold convolution of $F$ with itself and $C$ is an absolute constant. The paper contains the first part of the proof.
