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

 

Semiregular invariant measures on abelian groups


Author: Andrzej Pelc
Journal: Proc. Amer. Math. Soc. 86 (1982), 423-426
MSC: Primary 03E35; Secondary 03E55, 28C10
MathSciNet review: 671208
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Abstract: A nonnegative countably additive, extended real-valued measure is called semiregular if every set of positive measure contains a set of positive finite measure. V. Kannan and S. R. Raju [3] stated the problem of whether every invariant semiregular measure defined on all subsets of a group is necessarily a multiple of the counting measure. We prove that the negative answer is equivalent to the existence of a real-valued measurable cardinal.

It is shown, moreover, that a counterexample can be found on every abelian group of real-valued measurable cardinality.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0671208-4
PII: S 0002-9939(1982)0671208-4
Keywords: Universal invariant measure, group, real-valued measurable cardinal
Article copyright: © Copyright 1982 American Mathematical Society