A-ergodicity of probability measures on locally compact groups

Let G be a locally compact group with the left Haar measure m G and let A = a n , k n , k = 0 ∞ be a strongly regular matrix. We show that if μ is a power bounded measure on G , then there exists an idempotent measure θ μ such that w*- lim n → ∞ ∑ k = 0 ∞ a n , k μ k = θ μ . If μ is a probability me...

Full description

Saved in:
Bibliographic Details
Published in:Archiv der Mathematik 2024, Vol.122 (1), p.47-57
Main Author: Mustafayev, Heybetkulu
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Subgroups
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Let G be a locally compact group with the left Haar measure m G and let A = a n , k n , k = 0 ∞ be a strongly regular matrix. We show that if μ is a power bounded measure on G , then there exists an idempotent measure θ μ such that w*- lim n → ∞ ∑ k = 0 ∞ a n , k μ k = θ μ . If μ is a probability measure on a compact group G ,  then w*- lim n → ∞ ∑ k = 0 ∞ a n , k μ k = m ¯ H , where H is the closed subgroup of G generated by supp μ and m ¯ H is the measure on G defined by m ¯ H E : = m H E ∩ H for every Borel subset E of G .
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-023-01938-y