Geodesic
The principle of convergence “almost everywhere” in Lie groups
Sbornik. Mathematics, Tome 20 (1973) no. 4, pp. 543-555 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {The principle of convergence {\textquotedblleft}almost everywhere{\textquotedblright} in {Lie} groups},
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V. M. Maksimov. The principle of convergence “almost everywhere” in Lie groups. Sbornik. Mathematics, Tome 20 (1973) no. 4, pp. 543-555. http://geodesic.mathdoc.fr/item/SM_1973_20_4_a3/

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