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 Teor. Veroyatnost. i Primenen.: Year: Volume: Issue: Page: Find

 Teor. Veroyatnost. i Primenen., 1980, Volume 25, Issue 3, Pages 614–619 (Mi tvp1103)

Short Communications

Limit theorems of probability theory for compact topological groups

S. B. Šlosman

Moscow

Abstract: We find sufficient conditions for the distribution of the sum of nonidentically distributed elements of compact topological group to converge to the uniform distribution. This conditions generalize the previously known conditions for the weak convergence. We prove that convergence in variation takes place also and that under some additional regularity conditions the uniform convergence to the constant density takes place. For identically distributed summands the rate of convergence is exponential.

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English version:
Theory of Probability and its Applications, 1981, 25:3, 604–609

Bibliographic databases:

Revised: 19.06.1979

Citation: S. B. Šlosman, “Limit theorems of probability theory for compact topological groups”, Teor. Veroyatnost. i Primenen., 25:3 (1980), 614–619; Theory Probab. Appl., 25:3 (1981), 604–609

Citation in format AMSBIB
\Bibitem{Shl80} \by S.~B.~{\v S}losman \paper Limit theorems of probability theory for compact topological groups \jour Teor. Veroyatnost. i Primenen. \yr 1980 \vol 25 \issue 3 \pages 614--619 \mathnet{http://mi.mathnet.ru/tvp1103} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=582593} \zmath{https://zbmath.org/?q=an:0462.60011|0436.60013} \transl \jour Theory Probab. Appl. \yr 1981 \vol 25 \issue 3 \pages 604--609 \crossref{https://doi.org/10.1137/1125074} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980MB70100018}