On the automorphically stable distributions on Abelian groups

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Abstract

On a local compact Abelian group X, we consider G-automorphically stable distributions, where G is a subgroup of a group Aut(X). It is shown that if μ is G-automorphically stable, then 1) μ is either absolutely continuous, singular, or discrete with respect to the Haar measure of the group X; 2) if n is discrete, then μ 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 μ is a shift of the Haar distribution of a compact G-automorphically stable subgroup of the group X.

Original languageEnglish
Pages (from-to)512-517
Number of pages6
JournalTheory of Probability and its Applications
Volume45
Issue number3
DOIs
StatePublished - 1 Jan 2000
Externally publishedYes

Keywords

  • G-automorphically stable distributions and subgroups
  • G-characteristic subgroup
  • Haar distribution

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