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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
$$
\widetilde\xi_1+\widetilde\xi_2+\dots+\widetilde\xi_n+\cdots.
$$
Bibliography: 6 titles.
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
Linking options:
https://www.mathnet.ru/eng/sm3315https://doi.org/10.1070/SM1973v020n04ABEH001894 https://www.mathnet.ru/eng/sm/v133/i4/p523
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Abstract page: | 246 | Russian version PDF: | 111 | English version PDF: | 4 | References: | 26 |
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