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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The existence of universal invariant semiregular measures on groups
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by Piotr Zakrzewski PDF
Proc. Amer. Math. Soc. 99 (1987), 507-508 Request permission

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
  • © Copyright 1987 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 99 (1987), 507-508
  • MSC: Primary 43A05; Secondary 03E55, 28C10
  • DOI: https://doi.org/10.1090/S0002-9939-1987-0875389-3
  • MathSciNet review: 875389