%0 Journal Article
%T On uniform distribution in probability for sequences of products of independent random elements in a compact metric group
%A Sergey M. Dobrovolsky
%A Maria S. Dobrovolskaya
%J Uniform Distribution Theory
%D 2012
%I Mathematical Institute of the Slovak Academy of Sciences
%X We consider the concept of uniform distribution in probability forsequences of random elements in a compact metric group. We prove acriterion for uniform distribution in probability for sequences ofproducts of independent random elements. As a corollary, we obtaina criterion for uniform distribution modulo $1$ in probability forsequences of sums of independent random variables which generalizesthe classical Weyl's criterion.
%K Weyl's criterion
%K uniform distribution modulo $1$
%K uniform distribution almost surely
%K asymptotic uniformity in distribution $(mod 1)$
%K uniform distribution in probability
%K random elements in compact metric groups
%U http://www.boku.ac.at/MATH/udt/vol07/no2/04Dobro17-11.pdf