2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165808A recent result on size functions is extended to higher homology modules: the persistent homology based on a multidimensional measuring function is reduced to a 1-dimensional one. This leads to a stable distance for multidimensional persistent homology. Some reflections on i-essentiality of homological critical values conclude the paper.16 pages, 11 figuresAlgebraic Topology55N20; 68U05text