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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.


References [Enhancements On Off] (What's this?)

  • [E-M] P. Erdös and R. D. Mauldin, The nonexistence of certain invariant measures, Proc. Amer. Math. Soc. 59 (1976), 321-322. MR 0412390 (54:516)
  • [O] J. Oxtoby, Measure and category, A survey of the analogies between topological and measure spaces, Graduate Texts in Math., Vol. 2, Springer-Verlag, Berlin and New York, 1971. MR 0393403 (52:14213)
  • [R-T] C. Ryll-Nardzewski and R. Telgarsky, The nonexistence of universal invariant measures, Proc. Amer. Math. Soc. 69 (1978), 240-242. MR 0466494 (57:6372)

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Additional Information

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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