  This 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 $Dim(\bar{X}^{\alpha})$ 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 $Dim(\bar{X}^{\alpha})$.
