A note on the support of right invariant measures

Abstract

A regular measure μ on a locally compact topological semigroup is called right invariant if μ(Kx)=μ(K) for every compact K and x in its support. It is shown that this condition implies a property reminiscent of the right cancellation law. This is used to generalize a theorem of A. Mukherjea and the author (with a new proof) to the effect that the support of an r*-invariant measure is a left group iff the measure is right invariant on its support.