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 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. [ABSTRACT FROM AUTHOR]