2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76071Let (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.27 pagesOperator Algebras46L05, 46L39, 22D30, 57S05text