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Some problems on idempotent measures on semigroups

Published online by Cambridge University Press:  17 April 2009

N. A. Tserpes  and
A. Mukherjea
N. A. Tserpes
Affiliation:
University of South Florida, Tampa.
A. Mukherjea
Affiliation:
University of South Florida, Tampa.
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Abstract

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Essentially this paper does the following: In Section 2 it gives necessary and sufficient conditions in order that the support of an idempotent measure on a locally compact semigroup S, be completely simple. In Section 3 it proves that if I is an ideal of S of positive measure μ (= any probability measure), then μn (I) strictly increases to the limit 1. If in addition μ is idempotent, then μ (N-1N) and μ(NN-1) are positive for any open set N. In Section 4 certain compactness conditions are proven equivalent to joint weak*–continuity of the convolution of bounded measures and a limit theorem concerning the convolution powers (Cesarò sums) of μ is proven.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 2 , Issue 3 , June 1970 , pp. 299 - 315
Copyright
Copyright © Australian Mathematical Society 1970

References

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