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On r*-Invariant Measure on a Locally Compact Semigroup with Recurrence

A regular Borel measure μ is said to be r*-invariant on a locally compact semigroup if μ(Ba -1) = μ(B) for all Borel sets B and points a of S, where Ba -1 ={xϵS, xaϵB}. In [1] Argabright conjectured that the support of an r*-invariant measure on a locally compact semigroup is a left group, Mukherjea and Tserpes [4] proved this conjecture in the case that the measure is finite; however their method of proof fails when the measure is infinite.