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A semigroup is a set $S$ together with a binary operation that is associative. Examples of semigroups are the set of finite strings over a fixed alphabet (under concatenation) and the positive integers (under addition, maximum, or minimum). A monoid is a semigroup with a neutral element. Of course, any group is also a monoid/semigroup.

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Haar Measure on Locally Compact Semigroups

Existence of left invariant measures on a semigroup $S$ with definitions of $m(A)=m(xA)$ or $m({y:y \ \text{belongs to}\ xA})$ does not mean that support $m$ is a right group because it could be embed …
Sam Klevsky's user avatar