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Semigroups with invariant Radon measures


Author: Chandra Gowrisankaran
Journal: Proc. Amer. Math. Soc. 38 (1973), 400-404
MSC: Primary 28A70; Secondary 22A15, 43A05
DOI: https://doi.org/10.1090/S0002-9939-1973-0313480-0
MathSciNet review: 0313480
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Abstract: Let $ S$ be a commutative semigroup which is a topological space such that the translations are both continuous and open maps. The main result states that if (1) either $ S$ is Suslin such that there is at least one point of continuity for the semigroup mapping $ S \times S \to S$ or $ S$ is polish and (2) $ \exists $ a nontrivial Radon measure on $ S$ such that $ \mu (V) = \mu (x + V)$ for $ V$ open $ \subset S$ and $ x \in S$, then $ S$ can be embedded as an open subsemigroup of a locally compact group. It is also shown that if $ S$ is polish and a cancellation semigroup then $ S$ can be embedded as an open subsemigroup of a group.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0313480-0
Keywords: Polish, Suslin, semigroup, invariant measure, topological group, Haar measure, Radon measure
Article copyright: © Copyright 1973 American Mathematical Society

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