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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The existence of universal invariant semiregular measures on groups


Author: Piotr Zakrzewski
Journal: Proc. Amer. Math. Soc. 99 (1987), 507-508
MSC: Primary 43A05; Secondary 03E55, 28C10
MathSciNet review: 875389
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Abstract: A nonnegative, countably additive, extended real-valued measure is universal on a set $ X$ iff it is defined on all subsets of $ X$, and is semiregular iff every set of positive measure contains a subset of positive finite measure. We prove that on every group of sufficiently large cardinality there exists a universal invariant semiregular measure vanishing on singletons. Thus we give complete solutions to the problems stated by Kannan and Raju [4] and Pelc [5].


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0875389-3
PII: S 0002-9939(1987)0875389-3
Article copyright: © Copyright 1987 American Mathematical Society