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On measures integrating all functions of a given vector lattice

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Abstract

LetE be a vector lattice of real-valued functions defined on a setX, and ℋ(E):={{f⩾1}:f∈E}. Among others, it is shown that, under some additional assumptions onE, every measure that integrates all functionsf∈E is ϰ(E)-τ-smooth iffX is ϰ (E)-complete. An application of this general result to various topological situations yields some new measure-theoretic characterizations of realcompact, Borel-complete andN-compact spaces, respectively.

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  1. Mathamtisches Institut, Universität München, Theresienstrasse 39, D-8000, München 2, Federal Republic of Germany

    Wolfgang Adamski

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  1. Wolfgang Adamski
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Adamski, W. On measures integrating all functions of a given vector lattice. Monatshefte für Mathematik 103, 169–176 (1987). https://doi.org/10.1007/BF01364337

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  • DOI: https://doi.org/10.1007/BF01364337

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