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Proceedings of the American Mathematical Society

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

 

 

Continuous ergodic measures on $ R\sp{\infty }$ have disjoint powers


Author: Marek Kanter
Journal: Proc. Amer. Math. Soc. 65 (1977), 332-337
MSC: Primary 60G30
DOI: https://doi.org/10.1090/S0002-9939-1977-0443067-4
MathSciNet review: 0443067
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Abstract: If $ \mu $ is an ergodic probability measure on an infinite dimensional linear measure space and if there exists an infinite sequence of measurable linear functional on this space such that all nontrivial linear combinations have continuous distribution under $ \mu $, then the convolution powers of $ \mu $ all live on disjoint sets.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0443067-4
Keywords: Measure algebra, singular measures, generalized characters, convolution of measures
Article copyright: © Copyright 1977 American Mathematical Society