2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/212567The sequence of $α$-trimmings of empirical probabilities is shown to converge, in the Painlevé--Kuratowski sense, on the class of probability measures endowed with the weak topology, to the $α$-trimming of the population probability. Such a result is applied to the study of the asymptotic behaviour of central regions based on the trimming of a probability.Published in at http://dx.doi.org/10.3150/07-BEJ109 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)Statistics Theorytext