Invariant measures on locally compact semigroups

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 $S$.