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

 

Regularity of group valued Baire and Borel measures


Authors: K. Sundaresan and Peter W. Day
Journal: Proc. Amer. Math. Soc. 36 (1972), 609-612
MSC: Primary 28A45
MathSciNet review: 0306441
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Abstract: It is known that a real valued measure (1) on the $ \sigma $-ring of Baire sets of a locally compact Hausdorff space, or (2) on the Borel sets of a complete separable metric space is regular. Recently Dinculeanu and Kluvánek used regularity of nonnegative Baire measures to prove that any Baire measure with values in a locally convex Hausdorff topological vector space (TVS) is regular. Subsequently a direct proof of the same result was offered by Dinculeanu and Lewis. Here we show just as directly that any measure defined as in (1) or (2) is regular, even when it takes values in a Hausdorff topological group. In particular, when the group is a Hausdorff TVS, our result improves the Dinculeanu-Kluvánek-Lewis theorem.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0306441-8
PII: S 0002-9939(1972)0306441-8
Keywords: Regular measure, group valued measure, Baire measure, Borel measure
Article copyright: © Copyright 1972 American Mathematical Society