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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

$ M\sb{0}\,(G)$ is not a prime $ L$-ideal of measures


Author: Colin C. Graham
Journal: Proc. Amer. Math. Soc. 27 (1971), 557-562
MSC: Primary 42.56
DOI: https://doi.org/10.1090/S0002-9939-1971-0278007-9
MathSciNet review: 0278007
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Abstract: A technique of Hewitt and Zuckerman is used to show that if $ G$ is any locally compact abelian group with dual $ \Gamma $, then there exist nonzero positive regular Borel measures $ \mu ,v$ on $ G$, each one of which is mutually singular with each measure $ \omega $ whose Fourier-Stieltjes transform vanishes at infinity on $ \Gamma $ and such that the Fourier-Stieltjes transform of the convolution $ \mu \ast v$ vanishes at infinity on $ \Gamma $.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0278007-9
Keywords: Prime ideals of measures, Fourier-Stieltjes transforms
Article copyright: © Copyright 1971 American Mathematical Society