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A note on the idempotent measures on countable semigroups

Published online by Cambridge University Press:  09 April 2009

Tze-Chien Sun  and
N. A. Tserpes
Tze-Chien Sun
Affiliation:
Wayne State University and University of South Florida
N. A. Tserpes
Affiliation:
Wayne State University and University of South Florida
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In [6] we announced the following Conjecture: Let S be a locally compact semigroup and let μ be an idempotent regular probability measure on S with support F. Then

(a) F is a closed completely simple subsemigroup.

(b) F is isomorphic both algebraically and topologically to a paragroup ([2], p.46) X × G × Y where X and Y are locally compact left-zero and right-zero semi-groups respectively and G is a compact group. In X × G × Y the topology is the product topology and the multiplication of any two elements is defined by , x where [y, x′] is continuous mapping from Y × X → G.

(c) The induced μ on X × G × Y can be decomposed as a product measure μX × μG× μY where μX and μY are two regular probability measures on X and Y respectively and μG is the normed Haar measure on G.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 11 , Issue 4 , November 1970 , pp. 417 - 420
Copyright
Copyright © Australian Mathematical Society 1970

References

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