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”.
