2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/162494This article fits in many studies of multifractal analysis of measure. We took as a starting point the work of F. Ben Nasr in " Calculs de dimension de packing " to give a new inequality involving $Dim(\bar{X}^α)$ which would be, in certain cases, finer than the inequality established by L. Olsen in " A multifractal formalism " . Besides we elaborated an application of our result which gives a better inequality involving $Dim(\bar{X}^α)$.16pagesDynamical Systemstext