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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
Full-text PDF (474 kB) Citations (5)
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
English version:
Theory of Probability and its Applications, 1963, Volume 8, Issue 3, Pages 282–286
DOI: https://doi.org/10.1137/1108031
Document Type: Article
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Saz63}
\by V.~V.~Sazonov
\paper On the Glivenko--Cantelli Theorem
\jour Teor. Veroyatnost. i Primenen.
\yr 1963
\vol 8
\issue 3
\pages 299--303
\mathnet{http://mi.mathnet.ru/tvp4676}
\transl
\jour Theory Probab. Appl.
\yr 1963
\vol 8
\issue 3
\pages 282--286
\crossref{https://doi.org/10.1137/1108031}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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