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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.

UDC: 519.46

MSC: Primary 60B99, 60F99, 40A20; Secondary 43A80

Received: 07.12.1972

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

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