|
Teoriya Veroyatnostei i ee Primeneniya, 1963, Volume 8, Issue 3, Pages 299–303
(Mi tvp4676)
|
|
|
|
This article is cited in 5 scientific papers (total in 5 papers)
Short Communications
On the Glivenko–Cantelli Theorem
V. V. Sazonov Moscow
Abstract:
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.
Received: 24.02.1962
Citation:
V. V. Sazonov, “On the Glivenko–Cantelli Theorem”, Teor. Veroyatnost. i Primenen., 8:3 (1963), 299–303; Theory Probab. Appl., 8:3 (1963), 282–286
Linking options:
https://www.mathnet.ru/eng/tvp4676 https://www.mathnet.ru/eng/tvp/v8/i3/p299
|
|