2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128084In this paper we consider the question of whether the doubling character of a measure supported on a subset of $\RR^m$ determines the regularity of its support (in a classical sense). This problem was studied by David, Kenig and Toro for codimension 1 sets under the assumption that the support be flat. Here we study the higher codimension case and remove the flatness hypothesis.26 pages, 1 figureClassical Analysis and ODEsFunctional Analysis28A75, 49Q15, 58C35text