On measures integrating all functions of a given vector lattice |
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Authors: | Wolfgang Adamski |
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Institution: | (1) Mathamtisches Institut, Universität München, Theresienstrasse 39, D-8000 München 2, Federal Republic of Germany |
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Abstract: | LetE be a vector lattice of real-valued functions defined on a setX, and (E):={{f 1}:f E}. Among others, it is shown that, under some additional assumptions onE, every measure that integrates all functionsf E is (E)- -smooth iffX is (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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