Erich Klement, Siegfried Weber,
"An integral representation for decomposable measures of measurable functions"
, in Aequationes Mathematicae, Vol. 47, Nummer 2-3, Seite(n) 255-262, 1994, ISSN: 0001-9054
Original Titel:
An integral representation for decomposable measures of measurable functions
Sprache des Titels:
Englisch
Original Kurzfassung:
We start with a measure m on a measurable space (?, A), decomposable with respect to an Archimedean t-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 measure m on the space F 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 measure m on F can be represented as an integral of a certain Markov-kernel K.
We extend this representation to measures m~ on F 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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