Messbare Mengen von Massen und Inhalten |
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Authors: | Arnold Janssen |
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Institution: | (1) Abteilung Mathematik der Universität Dortmund, Postfach 50 05 00, D - 4600 Dortmund, West Germany |
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Abstract: | Let X be a completely regular space. The customary -field is the coarsest -field on the space of Bairemeasures on X which makes (A) measurable for any Baire set A. We compare the customary -field with the Baire and Borel -field induced by the weak* topology which lies on the dual space C(X). In (2.3) it is shown that the customary -field is just the Baire -field. In part 3 necessary and sufficient conditions are given under which the set of -smooth measures is measurable with respect to the Borel -field which lies on the positive cone of the space of finitely additive, regular measures C(X). Finally, a decomposition theorem for generalized kernels is proved. The -smooth part of a generalized kernel is a kernel again if certain conditions are fulfilled. |
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