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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
DOI: https://doi.org/10.1090/S0002-9939-1980-0556617-4
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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DOI: https://doi.org/10.1090/S0002-9939-1980-0556617-4
Keywords: Translation invariant measure, semiregular measure, $ \sigma $-finite measure
Article copyright: © Copyright 1980 American Mathematical Society

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