The nonexistence of invariant universal measures of semigroups
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- by V. Kannan and S. Radhakrishneswara Raju
- Proc. Amer. Math. Soc. 78 (1980), 482-484
- DOI: https://doi.org/10.1090/S0002-9939-1980-0556617-4
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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
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- John C. Oxtoby, Measure and category. A survey of the analogies between topological and measure spaces, Graduate Texts in Mathematics, Vol. 2, Springer-Verlag, New York-Berlin, 1971. MR 0393403, DOI 10.1007/978-1-4615-9964-7
- C. Ryll-Nardzewski and R. Telgársky, The nonexistence of universal invariant measures, Proc. Amer. Math. Soc. 69 (1978), no. 2, 240–242. MR 466494, DOI 10.1090/S0002-9939-1978-0466494-9
Bibliographic Information
- © Copyright 1980 American Mathematical Society
- 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