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.
Mathematics Subject Classifications (1991): 28A12, 28C15.
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References
Bauer, H.: Mass- und Integrationstheorie, 2. AuØ. de Gruyter, 1992.
Fremlin, D.H.: Topological measure theory: Two counter-examples. Math. Proc. Camb. Phil. Soc.78 (1995), 95±106.
KÈonig, H.: Measure and Integration: An Advanced Course in Basic Procedures and Applications Springer, 1997.
Schwartz, L.: Radon Measures on arbitrary Topological Spaces and Cylindrical Measures, Oxford Univ. Press, 1973.
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© 2012 Springer Basel
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König, H. (2012). Image measures and the so-called image measure catastrophe. In: Measure and Integration. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0382-3_1
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DOI: https://doi.org/10.1007/978-3-0348-0382-3_1
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Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0381-6
Online ISBN: 978-3-0348-0382-3
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