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Image measures and the so-called image measure catastrophe

  • Heinz König
Chapter

Abstract

The paper develops the formation of image measures on the basis of the recent monograph of the author 1997. The main theorem says that the structure of so-called inner extensions carries over from the initial measure to the image measure. One discloses the image measure catastrophe in the sense of Laurent Schwartz 1973 to be a lack of inner regularity on the part of the initial measure.

Keywords

image measure image measure catastrophe inner extensions of inner premeasures Lusin measurable 

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References

  1. 1.
    Bauer, H.: Mass- und Integrationstheorie, 2. AuØ. de Gruyter, 1992.Google Scholar
  2. 2.
    Fremlin, D.H.: Topological measure theory: Two counter-examples. Math. Proc. Camb. Phil. Soc.78 (1995), 95±106.zbMATHGoogle Scholar
  3. 3.
    KÈonig, H.: Measure and Integration: An Advanced Course in Basic Procedures and Applications Springer, 1997.Google Scholar
  4. 4.
    Schwartz, L.: Radon Measures on arbitrary Topological Spaces and Cylindrical Measures, Oxford Univ. Press, 1973.zbMATHGoogle Scholar

Copyright information

© Springer Basel 2012

Authors and Affiliations

  • Heinz König
    • 1
  1. 1.Fachbereich MathematikUniversität des SaarlandesSaarbrückenGermany

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