Radon measures on groups
Author:
Chandra Gowrisankaran
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
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Abstract | References | Similar Articles | Additional Information
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.
- Teng-sun Liu and Arnoud van Rooij, Transformation groups and absolutely continuous measures, Nederl. Akad. Wetensch. Proc. Ser. A 71=Indag. Math. 30 (1968), 225–231. 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 https://doi.org/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).
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© Copyright 1970
American Mathematical Society