PUB - Publikationen an der Universität Bielefeld

Consider a topological space T which is the union of a family of G-orbits, where G is a locally euclidean group G acting on T. On every G-orbit consider a probability which is absolutely continuous with respect to the image measure of the normalized restriction of the Haar measure on some compact neighborhood of the identity in G. Assume that the densities of the probabilities on the orbits have a common upper bound. Let [mu] be a probability on T which is the integral over the measures on the orbits with respect to some probability [mu]' on T. It is shown that this specific kind of integral representation of [mu] does not depend on the size of the compact neighborhood of the identity in G.