## Abstract

Let *G* be a locally compact group with the left Haar measure \(m_{G}\) and let \(A=\left[ a_{n,k}\right] _{n,k=0}^{\infty }\) be a strongly regular matrix. We show that if \(\mu \) is a power bounded measure on *G*, then there exists an idempotent measure \(\theta _{\mu }\) such that

If \(\mu \) is a probability measure on a compact group *G*, then

where *H* is the closed subgroup of *G* generated by \(\text{ supp }\mu \) and \( \overline{m}_{H}\) is the measure on *G* defined by \(\overline{m}_{H}\left( E\right) :=m_{H}\left( E\cap H\right) \) for every Borel subset *E* of *G*.

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The author is grateful to the referee for his helpful remarks and suggestions.

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Mustafayev, H. A-ergodicity of probability measures on locally compact groups.
*Arch. Math.* **122**, 47–57 (2024). https://doi.org/10.1007/s00013-023-01938-y

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DOI: https://doi.org/10.1007/s00013-023-01938-y