Geodesic
On the central limit theorem in $R^k$
Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 2, pp. 425-429 
V. V. Sazonov; V. G. Mirancev. On the central limit theorem in $R^k$. Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 2, pp. 425-429. http://geodesic.mathdoc.fr/item/TVP_1978_23_2_a19/
@article{TVP_1978_23_2_a19,
     author = {V. V. Sazonov and V. G. Mirancev},
     title = {On the central limit theorem in $R^k$},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {425--429},
     year = {1978},
     volume = {23},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1978_23_2_a19/}
}
TY  - JOUR
AU  - V. V. Sazonov
AU  - V. G. Mirancev
TI  - On the central limit theorem in $R^k$
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 1978
SP  - 425
EP  - 429
VL  - 23
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TVP_1978_23_2_a19/
LA  - ru
ID  - TVP_1978_23_2_a19
ER  - 
%0 Journal Article
%A V. V. Sazonov
%A V. G. Mirancev
%T On the central limit theorem in $R^k$
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1978
%P 425-429
%V 23
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1978_23_2_a19/
%G ru
%F TVP_1978_23_2_a19

Voir la notice de l'article provenant de la source Math-Net.Ru

An estimate of the rate of convergence in the central limit theorem in $R^k$ for i. i. d. summands in the spirit of [1] is obtained. The difference of the present estimate from that of [1] is in the dependence of the right side of it on the distribution of a summand. This dependence now ameliorates as the number of summands increases. In the one-dimensional case a similar result was obtained in [2].