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On the inner Daniell-Stone and Riesz representation theorems

  • Heinz KönigEmail author
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Abstract

The paper deals with the context of the inner Daniell- Stone and Riesz representation theorems, which arose within the new development in measure and integration in the book 1997 and subsequent work of the author. The theorems extend the traditional ones, in case of the Riesz theorem to arbitrary Hausdorff topological spaces. The extension enforces that the assertions attain different forms. The present paper wants to exhibit special situations in which the theorems retain their familiar appearance.

Keywords

Inner extensions inner premeasures Radon measures Radon premeasures positive (=isotone) linear functionals inner sources inner preintegrals Radon preintegrals tightness theorem of Kisyński 

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Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.MathematikUniversität des SaarlandesSaarbrückenGermany

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