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Mat. Sb. (N.S.), 1973, Volume 91(133), Number 4(8), Pages 523–536 (Mi msb3315)  

This article is cited in 1 scientific paper (total in 1 paper)

The principle of convergence “almost everywhere” in Lie groups

V. M. Maksimov


Abstract: Let $U$ be a neighborhood of the identity in an arbitrary Lie group with a fixed system of local coordinates $(x)$ and let $\xi_n$ be independent random variables taking values in the neighborhood $U$ and $\widetilde\xi_n$ be real variables naturally induced by the variables $\xi_n$ in the system of local coordinates $(x)$. If the $\widetilde\xi_n$ have zero means, then the product $\xi_1\cdots\xi_n$, $n\to\infty$, converges or diverges a.e. with
$$ \widetilde\xi_1+\widetilde\xi_2+…+\widetilde\xi_n+\cdots. $$

Bibliography: 6 titles.

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English version:
Mathematics of the USSR-Sbornik, 1973, 20:4, 543–555

Bibliographic databases:

UDC: 519.46
MSC: Primary 60B99, 60F99, 40A20; Secondary 43A80
Received: 07.12.1972

Citation: V. M. Maksimov, “The principle of convergence “almost everywhere” in Lie groups”, Mat. Sb. (N.S.), 91(133):4(8) (1973), 523–536; Math. USSR-Sb., 20:4 (1973), 543–555

Citation in format AMSBIB
\Bibitem{Mak73}
\by V.~M.~Maksimov
\paper The principle of convergence ``almost everywhere'' in Lie groups
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 91(133)
\issue 4(8)
\pages 523--536
\mathnet{http://mi.mathnet.ru/msb3315}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=372936}
\zmath{https://zbmath.org/?q=an:0297.60008}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 20
\issue 4
\pages 543--555
\crossref{https://doi.org/10.1070/SM1973v020n04ABEH001894}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. M. Maksimov, “Three-series theorems for locally compact groups”, Math. USSR-Sb., 45:2 (1983), 225–241  mathnet  crossref  mathscinet  zmath
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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