Strength of convergence in the orbit space of a transformation group ✩

Let (G,X) be a second-countable transformation group with G acting freely on X. It is shown that measure-theoretic accumulation of the action and topological strength of convergence in the orbit space X/G provide equivalent ways of quantifying the extent of nonproperness of the action. These notions are linked via the representation theory of the transformation-group C∗-algebra C0(X) G. © 2005 Elsevier Inc. All rights reserved.