Geodesic
On the Glivenko--Cantelli Theorem
Teoriâ veroâtnostej i ee primeneniâ, Tome 8 (1963) no. 3, pp. 299-303

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

It is found that the Glivenko–Cantelli theorem does not admit a generalisation to the infinite dimensional case. In fact under general conditions, with probability one the empirical distributions do not converge to the theoretical distribution uniformly on all half-spaces. Sufficient conditions for the validity of uniform convergence over a family of half-spaces with probability one are given. 
@article{TVP_1963_8_3_a4,
     author = {V. V. Sazonov},
     title = {On the {Glivenko--Cantelli} {Theorem}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {299--303},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {1963},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1963_8_3_a4/}
}
TY  - JOUR
AU  - V. V. Sazonov
TI  - On the Glivenko--Cantelli Theorem
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 1963
SP  - 299
EP  - 303
VL  - 8
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_1963_8_3_a4/
LA  - ru
ID  - TVP_1963_8_3_a4
ER  - 
%0 Journal Article
%A V. V. Sazonov
%T On the Glivenko--Cantelli Theorem
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1963
%P 299-303
%V 8
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_1963_8_3_a4/
%G ru
%F TVP_1963_8_3_a4
V. V. Sazonov. On the Glivenko--Cantelli Theorem. Teoriâ veroâtnostej i ee primeneniâ, Tome 8 (1963) no. 3, pp. 299-303. http://geodesic.mathdoc.fr/item/TVP_1963_8_3_a4/