On the convolution equation 𝑃=𝑃𝑄 of Choquet and Deny for probability measures on semigroups

Abstract

In this paper, the problem of determining regular probability measures P and Q satisfying P = P ∗ Q = Q ∗ P P = P ^\ast Q = Q ^\ast P has been solved on locally compact cancellative semigroups. The results also hold in the complete metric case. The results have been used to determine the primitive idempotent measures on locally compact semigroups.