Abstract
It is the purpose of this paper to characterize the complete spaces in the sense of [6] by measure-theoretic properties. Let (X,
) be a measurable space and let
be a subpaving of
satisfying certain closure properties, then X is
-complete iff every 0,1-valued
-regular measure on
is a Dirac measure. In particular, we obtain Hewitt's well-known theorem that a completely regular space X is realcompact iff every 0,1-valued Baire measure on X is a Dirac measure. The main tool for our investigations is an extension theorem for measures due to Topsoe [10].
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Adamski, W. Complete spaces and zero-one measures. Manuscripta Math 18, 343–352 (1976). https://doi.org/10.1007/BF01270495
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DOI: https://doi.org/10.1007/BF01270495