On the automorphically stable distributions on Abelian groups
Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 3, pp. 584-589
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On a local compact Abelian group $X$, we consider {$G$-auto}-morphically stable distributions, where $G$ is a subgroup of a group $Aut(X)$. It is shown that if $\mu$ is $G$-automorphically stable, then 1) $\mu$ is either absolutely continuous, singular, or discrete with respect to the Haar measure of the group $X$; 2) if $\mu$ is discrete, then $\mu$ is a shift of the Haar distribution of a finite $G$-characteristic subgroup of the group $X$; 3) if $G$ consists of elements of finite order, then $\mu$ is a shift of the Haar distribution of a compact $G$-automorphically stable subgroup of the group $X$.
Keywords:
$G$-automorphically stable distributions and subgroups, $G$-characteristic subgroup, Haar distribution.
@article{TVP_2000_45_3_a9,
author = {S. S. Gabrielyan},
title = {On the automorphically stable distributions on {Abelian} groups},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {584--589},
publisher = {mathdoc},
volume = {45},
number = {3},
year = {2000},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2000_45_3_a9/}
}
S. S. Gabrielyan. On the automorphically stable distributions on Abelian groups. Teoriâ veroâtnostej i ee primeneniâ, Tome 45 (2000) no. 3, pp. 584-589. http://geodesic.mathdoc.fr/item/TVP_2000_45_3_a9/