Three-series theorems for locally compact groups

This article deals with conditions for the convergence of the product $\prod\limits_1^\infty\xi_n$ of independent random variables $\xi_n$ taking values in an arbitrary locally compact group $G$. For various types of groups necessary and sufficient conditions are given for the convergence of this product almost everywhere, expressed in terms of the group $G$. They can be regarded as analogues of the classical three-series theorem.
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