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 non-properness of the action. These notions are linked via the representation theory of the transformation-group C*-algebra. 
Robert Archbold (University of Aberdeen), Astrid an Huef (University   of New South Wales)