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On central primitive idempotent measures
Published online by Cambridge University Press: 09 April 2009
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Let S be a compact semitopological semigroup and let P(S) be the convolution semigroup of probability measures on S. An idempotent measure μ in P(S) is defined to be primitive if and only idempotent measures in μP(S)μ are μ and the zero element m of P(S). In a previous paper [2] we give some characterization of primitive idempotent measures on S. Let Π(P(S)) be the set of primitive idempotents in P(S) and let Πc be the set of central primitive idempotents in P(S). It is shown in [1] that Π(P(S)) is neither an ideal nor even a subsemigroup of P(S) in general. The purpose of this paper is to investigate the structure of Πc.
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- Copyright © Australian Mathematical Society 1973
References
[1]Choy, S. T. L., ‘Idempotent measures on compact semi-groups’, Proc. London Math. Soc. (3) 20 (1970), 717–733.CrossRefGoogle Scholar
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