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.
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References
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König, 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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König, H. Image Measures and the So-Called Image Measure Catastrophe. Positivity 1, 255–270 (1997). https://doi.org/10.1023/A:1009708010838
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DOI: https://doi.org/10.1023/A:1009708010838