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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The strong conclusion of the F. and M. Riesz theorem on groups


Author: I. Glicksberg
Journal: Trans. Amer. Math. Soc. 285 (1984), 235-240
MSC: Primary 43A17; Secondary 43A25, 46J10
MathSciNet review: 748839
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Abstract: Let $ S$ be a closed proper generating subsemigroup of the dual $ \Gamma $ of a locally compact abelian group $ G$. Then there are Haar singular measures on $ G$ orthogonal to $ S$ unless $ G = {\mathbf{R}} \times \Delta $ or $ {\mathbf{T}} \times \Delta $ with $ \Delta $ discrete, and then all $ \mu $ orthogonal to $ S$ are Haar absolutely continuous.


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DOI: https://doi.org/10.1090/S0002-9947-1984-0748839-2
Article copyright: © Copyright 1984 American Mathematical Society