Chapter 5: Decomposable measures

Abstract

The main purpose of this chapter is to discuss the extent to which Theorem 4.3 can be generalized to arbitrary Radon measures (rather than probability measures) and to cases where G is not compact. Such generalizations can be used in the derivation of densities of maximal invariants as well as in other areas. The approach here is modelled after that described in Andersson (1982). Other possible approaches to this problem are described in Wijsman (1986) (the global cross section approach using some Lie group theory) and Farrell (1985) (a measure-theoretic cross section approach developed by Schwartz (1966), unpublished).