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Proceedings of the American Mathematical Society

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Finite Borel measures on spaces of cardinality less than $ \mathfrak{c}$


Authors: R. J. Gardner and G. Gruenhage
Journal: Proc. Amer. Math. Soc. 81 (1981), 624-628
MSC: Primary 54H99; Secondary 03E15, 04A15, 28A12, 54D20, 54G20
DOI: https://doi.org/10.1090/S0002-9939-1981-0601743-5
MathSciNet review: 601743
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Abstract: Let $ \kappa < c$ be uncountable. We prove, among other results, that every $ \alpha $-realcompact space of cardinality $ \kappa $ is Borel measure-compact if and only if there is a set of reals of cardinality $ \kappa $ whose Lebesgue measure is not zero.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0601743-5
Keywords: Borel measure, regular measure, Borel-complete space, measure-compact space, $ \alpha $-real compact space, Martin's axiom
Article copyright: © Copyright 1981 American Mathematical Society