Radon measures on groups
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- by Chandra Gowrisankaran
- Proc. Amer. Math. Soc. 25 (1970), 381-384
- DOI: https://doi.org/10.1090/S0002-9939-1970-0255724-7
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Abstract:
Let $G$ be a Hausdorff topological group with a nontrivial mobile real valued Radon measure. Then $G$ is locally compact. In particular if there is a nontrivial translation invariant Radon measure on $G$, then $G$ is locally compact.References
- Teng-sun Liu and Arnoud van Rooij, Transformation groups and absolutely continuous measures, Indag. Math. 30 (1968), 225–231. Nederl. Akad. Wetensch. Proc. Ser. A 71. MR 0227365
- John C. Oxtoby, Invariant measures in groups which are not locally compact, Trans. Amer. Math. Soc. 60 (1946), 215–237. MR 18188, DOI 10.1090/S0002-9947-1946-0018188-5 L. Schwartz, Lectures on Radon measures in Hausdorff topological spaces, Tata. Inst. of Fundamental Research Monographs (to appear).
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 25 (1970), 381-384
- MSC: Primary 22.10; Secondary 28.00
- DOI: https://doi.org/10.1090/S0002-9939-1970-0255724-7
- MathSciNet review: 0255724