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Proceedings of the American Mathematical Society

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Invariant measures on locally compact semigroups

Author: Roger Rigelhof
Journal: Proc. Amer. Math. Soc. 28 (1971), 173-176
MSC: Primary 28.75; Secondary 42.00
MathSciNet review: 0277691
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Abstract: The main result of this paper shows that a locally compact abelian semigroup is embeddable as an open subsemigroup of a locally compact abelian group $G$ if and only if the translations $x \mapsto x + y$ are open maps and there exists a nonnegative regular measure $\mu$ on $S$ such that $\mu (U) = \mu (x + U) > 0$ for every open set $U$ and $x$ in $S$.

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Keywords: Invariant measures, Haar measures, locally compact abelian semigroups, topological semigroups
Article copyright: © Copyright 1971 American Mathematical Society