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This article fits in many studies of multifractal analysis of measure. Wetook as a starting point the work of F. Ben Nasr in " Calculs de dimension depacking " to give a new inequality involving $Dim(\bar{X}^{\alpha})$ whichwould be, in certain cases, finer than the inequality established by L. Olsenin " A multifractal formalism " . Besides we elaborated an application of ourresult which gives a better inequality involving $Dim(\bar{X}^{\alpha})$.

Multifractal Formalism and Inequality involving Packing Dimension