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International Journal of Mathematics and Mathematical Sciences
Volume 15, Issue 2, Pages 405-408

A note on the support of right invariant measures

Department of Mathematics, University of Patra, Patra, Greece

Received 6 June 1990

Copyright © 1992 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.