Geodesic
Topology in a~Group and Convergence of Distributions
Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 1, pp. 122-125

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The purpose of this paper is to prove the following result. Let $\xi_1,\xi_2,\dots,\xi_n,\dots$ be an arbitrary sequence of independent random variables on a locally compact group $G$. We construct the compositions $$ \xi_n=\xi_1\xi_2\dots\xi_n. $$ If elements $a_n\in G$ can be found so that the sequence of normalized compositions $$ \eta_n=\zeta_n a_n $$ as a limiting distribution, then the group $G$ is compact. 
@article{TVP_1964_9_1_a12,
     author = {B. M. Kloss},
     title = {Topology in {a~Group} and {Convergence} of {Distributions}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {122--125},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {1964},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1964_9_1_a12/}
}
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B. M. Kloss. Topology in a~Group and Convergence of Distributions. Teoriâ veroâtnostej i ee primeneniâ, Tome 9 (1964) no. 1, pp. 122-125. http://geodesic.mathdoc.fr/item/TVP_1964_9_1_a12/