Mackey analysis of infinite classical motion groups

Representation theory for infinite classical motion groups is formulated in terms of invariant measure classes and cocycle cohomology. It is shown that invariant measure classes are always represented by invariant probability measures, and these classes are determined for Cartan motion groups. The existence of "induced" cocycle cohomology is established in this ergodic setting. Also it is shown that the continuity properties of representations are rather rigidly determined.