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Journal Article

Semiregular Invariant Measures on Abelian Groups

Andrzej Pelc
Proceedings of the American Mathematical Society
Vol. 86, No. 3 (Nov., 1982), pp. 423-426
DOI: 10.2307/2044441
Stable URL: http://www.jstor.org/stable/2044441
Page Count: 4

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Topics: Cardinality, Mathematical problems, Mathematical set theory, Mathematics
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Semiregular Invariant Measures on Abelian Groups
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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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