Absolutely Continuous and Locally Quasi-Invariant Measures on Locally Compact Semigroups

Henry A. M. Dzinotyiweyi

doi:10.2307/2043186

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Absolutely Continuous and Locally Quasi-Invariant Measures on Locally Compact Semigroups

Henry A. M. Dzinotyiweyi

Year: 1978 Journal: Proceedings of the American Mathematical Society Vol: 69 (1)Pages: 49-49 Publisher: American Mathematical Society

DOI: 10.2307/2043186

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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 â€™reasonably largeâ€™, 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.

Keywords:

Absolute continuity Locally compact space Locally compact group Mathematics Compact space Semigroup Pure mathematics Invariant (physics) Measure (data warehouse) Riesz–Markov–Kakutani representation theorem Discrete mathematics Computer science Mathematical physics

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advanced mathematical theories

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Absolutely Continuous and Locally Quasi-Invariant Measures on Locally Compact Semigroups

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