Let G be a second-countable locally-compact Hausdorff groupoid with a Haar system, and let { x_n} be a sequence in the unit space of G. We show that the notions of strength of convergence of { x_n} in the orbit space and measure-theoretic accumulation along the orbits are equivalent ways of realising multiplicity numbers associated to a sequence of induced representation of the groupoid C*-algebra.
Categories: math.OA