An integral representation for decomposable measures of measurable functions |
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Authors: | Erich Peter Klement Siegfried Weber |
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Institution: | (1) Institut für Mathematik, Johannes Kepler Universität, A-4040 Linz, Austria;(2) Fachbereich Mathematik, Johannes Gutenberg-Universität, Mainz, Germany |
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Abstract: | Summary We start with a measurem on a measurable space (,A), decomposable with respect to an Archimedeant-conorm on a real interval 0,M], which generalizes an additive measure. Using the integral introduced by the second author, a Radon-Nikodym type theorem, needed in what follows, is given.The integral naturally leads to a -decomposable measurem on the space of all measurable functions from to 0, 1]. The main result of the present paper is the converse of this, namely that, under natural conditions, any -decomposable measurem on can be represented as an integral of a certain Markov-kernelK.
We extend this representation to measures
on which have values in a set of distribution functions.These results generalize the work done by the first author in the case of additive measures. |
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Keywords: | Primary 28B10 Secondary 39B40 |
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