Abstract

The problem of defining vector-valued probability measures on a compact semitopological semigroup S is considered in this paper. The set PW( S, A) of all such A-valued measures, analogous to the scalar-valued measures, is a compact semitopological semigroup with respect to the convolution operation and the weak operator topology. Supports of idempotents and the limits of averaged convolution sequences in PW( S, A) are determined.

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