Geodesic
On the Glivenko–Cantelli Theorem
Teoriâ veroâtnostej i ee primeneniâ, Tome 8 (1963) no. 3, pp. 299-303 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {V. V. Sazonov},
     title = {On the {Glivenko{\textendash}Cantelli} {Theorem}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {299--303},
     year = {1963},
     volume = {8},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1963_8_3_a4/}
}
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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/