The disintegration of invariant measures

Abstract

Krickeberg (in (5) and (6)) showed that disintegration applied to invariant measures sometimes yields an integral representation which is useful in analysing the moment measures of point processes. His results, based on Bourbaki's disintegration theory, raised several questions. We refine the theory, using a more general disintegration theorem, and answer his questions by several examples. Finally we consider how far the enlarged theory is applicable in stochastic geometry.