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Proceedings of the American Mathematical Society

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

 

 

On the regularity of measures on locally compact spaces


Authors: Mark Levin and Wilbur Stiles
Journal: Proc. Amer. Math. Soc. 36 (1972), 201-206
MSC: Primary 28A32
MathSciNet review: 0316660
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Abstract: The purpose of this paper is to present the two following theorems:

(1) Every Baire measure on the $ \sigma $-algebra $ {\mathcal{B}_a}$ generated by the compact $ {\mathcal{G}_\delta }$ subsets of a paracompact, locally compact space is outer regular; (2) in a paracompact, locally compact space, any Baire measure on $ {\mathcal{B}_a}$ can be extended to an outer regular Borel measure on the $ \sigma $-algebra generated by the closed subsets.

In addition, this paper contains an example which shows that neither of these two theorems is true for all arbitrary locally compact Hausdorff spaces.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0316660-2
Keywords: Baire measure, Borel measure, outer regular measure, locally compact space, paracompact space
Article copyright: © Copyright 1972 American Mathematical Society