Geodesic
On convergence of the products of independents random variables on a finite group
Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 4, pp. 678-697 Cet article a éte moissonné depuis la source Math-Net.Ru

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The notion of variance for random variables on a finite group $G$ as a numerical function is axiomatically introduced. The variance is applied to study questions of convergence of the product of random variables on $G$. In particular the following theorem is proved: if $x_1(\omega),\dots,x_n(\omega)$, are independent random variables on a group $G$ then for $z_n(\omega)=x_1(\omega),\dots,x_n(\omega)$ to converge almost everywhere the necessary and sufficient conditions are that distributions of $x_n(\omega)$ tend to the distribution concentrated on the unit of $G$ and the series of variances for the sequence $x_1(\omega),\dots,x_n(\omega),\dots$ converge. 
@article{TVP_1967_12_4_a6,
     author = {V. M. Maksimov},
     title = {On convergence of the products of independents random variables on a~finite group},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {678--697},
     year = {1967},
     volume = {12},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1967_12_4_a6/}
}
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V. M. Maksimov. On convergence of the products of independents random variables on a finite group. Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 4, pp. 678-697. http://geodesic.mathdoc.fr/item/TVP_1967_12_4_a6/