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


Author: A. Mukherjea
Journal: Proc. Amer. Math. Soc. 32 (1972), 457-463
MSC: Primary 60B15
DOI: https://doi.org/10.1090/S0002-9939-1972-0293687-0
MathSciNet review: 0293687
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Abstract: In this paper, the problem of determining regular probability measures P and Q satisfying $ 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.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0293687-0
Keywords: Locally compact topological semigroup, regular measure, convolution of measures, normed Haar measure
Article copyright: © Copyright 1972 American Mathematical Society