Quasi-invariant Radon measures on groups

Gowrisankaran, Chandra

doi:10.1090/S0002-9939-1972-0318777-5

Quasi-invariant Radon measures on groups
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Proc. Amer. Math. Soc. 35 (1972), 503-506 Request permission

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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