Three-series theorems for locally compact groups

V. M. Maksimov


Abstract: 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.
Bibliography: 14 titles

UDC: 519.21

MSC: Primary 22D05, 60B15, 60G50; Secondary 22E99, 60B10, 60F20

Received: 09.03.1981

 English version: Mathematics of the USSR-Sbornik, 1983, 45:2, 225–241

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