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Nilpotent measures on compact semigroups

Published online by Cambridge University Press:  17 April 2009

H.L. Chow
H.L. Chow
Affiliation:
Department of Mathematics, Chung Chi College, The Chinese University of Hong Kong, Hong Kong.
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Abstract

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Let S be a compact semigroup and P(S) the set of probability measures on S. Suppose P(S) has zero θ and define a measure μ ε P(S) nilpotent if μn → θ. It is shown that any measure with support containing that of θ is nilpotent, and the set of nilpotent measures is convex and dense in P(S). A measure μ is called mean-nilpotent if (μ + μ2 + … + μn)/n → θ, and can be characterized in terms of its support.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 1 , February 1975 , pp. 149 - 153
Copyright
Copyright © Australian Mathematical Society 1975

References

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