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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Quasi-invariant Radon measures on groups


Author: Chandra Gowrisankaran
Journal: Proc. Amer. Math. Soc. 35 (1972), 503-506
MSC: Primary 43A05; Secondary 28A40, 46G05
MathSciNet review: 0318777
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Abstract: Let G be a Hausdorff topological group which is a Baire space. It is proved that if there is a quasi-invariant Radon measure on G then G is locally compact. Examples of non-Baire groups with and without quasi-invariant measures are considered. In particular, it is shown that there is no $ \sigma $-finite measure on the Wiener space which preserves sets of measure zero under translation.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0318777-5
PII: S 0002-9939(1972)0318777-5
Keywords: Topological group, quasi-invariant, Radon measure, locally compact, Baire space, vector space, Wiener algebra
Article copyright: © Copyright 1972 American Mathematical Society