2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/218385In this paper we prove almost sure convergence to the ball, in the Nikodym metric, of sequences of random Steiner symmetrizations of bounded Caccioppoli and bounded measurable sets, paralleling a result due to Mani-Levitska concerning convex bodies.15 pages, submittedProbabilityFunctional Analysis60D05 (Primary) 52A40 (Secondary)text