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Absolutely continuous and locally quasi-invariant measures on locally compact semigroups


Author: Henry A. M. Dzinotyiweyi
Journal: Proc. Amer. Math. Soc. 69 (1978), 49-55
MSC: Primary 22A20; Secondary 43A05
DOI: https://doi.org/10.1090/S0002-9939-1978-0476907-4
MathSciNet review: 0476907
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Abstract: Let S be a locally compact semigroup and T a locally compact subsemigroup of S. It is shown that, for a large class of semigroups S, if T is 'reasonably large', the absolutely continuous measures on T extend to measures whose translates by some points of S are absolutely continuous on S. As a consequence we prove the absolute continuity of translates of some measures related to a locally quasi-invariant measure.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0476907-4
Keywords: Absolutely continuous measure, locally quasi-invariant measure, translate of a measure, foundation semigroup
Article copyright: © Copyright 1978 American Mathematical Society

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