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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Idempotent measures on locally compact semigroups


Authors: A. Mukherjea and N. A. Tserpes
Journal: Proc. Amer. Math. Soc. 29 (1971), 143-150
MSC: Primary 22A20; Secondary 46G99
DOI: https://doi.org/10.1090/S0002-9939-1971-0296207-9
MathSciNet review: 0296207
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Abstract: A conjecture that the support of an $ {r^ \ast }$-invariant regular finite measure on a locally compact semigroup is a left group is proven. Moreover we also prove that the support of an idempotent measure on a locally compact semigroup is completely simple, thus extending a well-known result of Pym and Heble-Rosenblatt on compact semigroups to the locally compact case. These results are also shown to be true in a complete metric semigroup.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0296207-9
Keywords: Locally compact topological semigroup, regular Borel measure, idempotent measure, completely simple semigroup, right invariant measure
Article copyright: © Copyright 1971 American Mathematical Society