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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Radon measures on groups

Author: Chandra Gowrisankaran
Journal: Proc. Amer. Math. Soc. 25 (1970), 381-384
MSC: Primary 22.10; Secondary 28.00
MathSciNet review: 0255724
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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.

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  • [1] T. S. Liu and A. van Rooij, Transformation groups and absolutely continuous measures, Nederl. Akad. Wetensch. Proc. Ser. A 71 = Indag. Math. 30 (1968), 225231. MR 37 #2950. MR 0227365 (37:2950)
  • [2] J. C. Oxtoby, Invariant measures in groups which are not locally compact, Trans. Amer. Math. Soc. 60 (1946), 215-237. MR 8, 253. MR 0018188 (8:253d)
  • [3] L. Schwartz, Lectures on Radon measures in Hausdorff topological spaces, Tata. Inst. of Fundamental Research Monographs (to appear).

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