Idempotent measures on locally compact semigroups

Mukherjea, A.; Tserpes, N. A.

doi:10.1090/S0002-9939-1971-0296207-9

Idempotent measures on locally compact semigroups
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by A. Mukherjea and N. A. Tserpes PDF

Proc. Amer. Math. Soc. 29 (1971), 143-150 Request permission

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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