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What are signed contents and measures?

  • Heinz KönigEmail author
Chapter
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Abstract

The paper develops the notion of signed contents and measures on the basis of a new definition. It forms a common roof for some well - known partial notions which appeared to be incompatible. The paper also redefines the notion of singular pairs of contents and measures, to the effect that the two notions are connected via an extended Jordan decomposition theorem. The decisive idea is a new difference formation for contents and measures.

Keywords

Signed contents and measures singular pairs of contents and measures lattice singular difference formation for contents and measures inner regular Godement-Bourbaki theorem 

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References

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    Fremlin, D. H.: Topological Measure Theory; Two Counter-Examples, Math. Proc. Camb. Phil. Soc. 78 (1975), 95–106CrossRefGoogle Scholar
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    Guillerme, J.: Remarques sur l'Ensemble Ordonné des Mesures Abstraites. In: Séminaire Initiation à l'Analyse (G. Choquet, M. Rogalski, J. Saint Raymond), Univ. Paris 6, 20ème Année 1980/81, no. 1, 8 pp.Google Scholar
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    König, H.: Measure and Integration: An Advanced Course in Basic Procedures and Applications, Springer–Verlag, 1997 Math. Nachr. 204 (1999)Google Scholar
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    Schwartz, L.: Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures, Oxford Univ. Press, 1973Google Scholar

Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.Fachbereich MathematikUniversität des SaarlandesSaarbrückenGermany

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