Vol. 91, No. 1, 1980

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Direct factorizations of measures

Karl-Theodor Eisele

Vol. 91 (1980), No. 1, 79–93

In this paper we want to investigate the question, to what extent can the disintegration of some measure on an arbitrary Suslin space with respect to some measurable function f be replaced by the image measure under some function g inverting f, such that the “outcome” of the situation under a function h is not changed. Such a direct factorization, as we call it, is modulo some conditions about atoms of the measures in general only possible, if the range of h is countable. But there are always solutions to the problem in a weak sense. The results have applications in game theory to the problem of “elimination of randomization”.

Mathematical Subject Classification 2000
Primary: 28A12
Secondary: 28A50, 90D10
Received: 31 July 1979
Revised: 29 November 1979
Published: 1 November 1980
Karl-Theodor Eisele