A characterisation of absolutely continuous measures on topological semigroups
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- by Heneri A. M. Dzinotyiweyi PDF
- Proc. Amer. Math. Soc. 121 (1994), 1103-1109 Request permission
Abstract:
Let S be a completely regular topological semigroup and $\mu$ a bounded regular Borel measure on S. For a very large class of noncompact semigroups S, we show that the map $x \to {\mu ^ \ast }\bar x$ of S into the space of bounded regular Borel measures on S is norm-continuous if and only if ${\mu _0}f$ is a left uniformly continuous function on S, for all bounded continuous functions f on S. Here the function ${\mu _0}f$ is given by \[ {\mu _0}f(x): = \int {f(yx)d\mu (y)\quad {\text {on}}\;S.} \]References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 121 (1994), 1103-1109
- MSC: Primary 22A10; Secondary 43A05
- DOI: https://doi.org/10.1090/S0002-9939-1994-1189541-7
- MathSciNet review: 1189541