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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The nonexistence of invariant universal measures of semigroups

Authors: V. Kannan and S. Radhakrishneswara Raju
Journal: Proc. Amer. Math. Soc. 78 (1980), 482-484
MSC: Primary 28C10; Secondary 20M99
MathSciNet review: 556617
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Abstract: We prove that if S is an uncountable subsemigroup of a group, then every (left or right)-translation invariant $\sigma$-finite measure defined on all subsets of S must be trivial. This answers a question posed by Ryll-Nardzewski and Telgarsky.

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Keywords: Translation invariant measure, semiregular measure, <IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\sigma$">-finite measure
Article copyright: © Copyright 1980 American Mathematical Society