2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210550In this paper we prove that, given s> 0, if E is a subset of R^m with positive and bounded s-dimensional Hausdorff measure H^s and the principal values of the s-dimensional signed Riesz transform of H^s|E exist H^s-almost everywhere in E, then s is integer. Other more general variants of this result are also proven.Classical Analysis and ODEsFunctional Analysis28A75; 31B10; 42B25text