  In this paper we study the existence of Lelong numbers of $m-$subharmonic
currents of bidimension $(p,p)$ on an open subset of $\Bbb C^n$, when $m+p\geq
n$. In the special case of $m-$subharmonic function $\varphi$, we give a
relationship between the Lelong numbers of $dd^c\varphi$ and the mean values of
$\varphi$ on spheres or balls. As an application we study the integrability
exponent of $\varphi$. We express the integrability exponent of $\varphi$ in
terms of volume of sub-level sets of $\varphi$ and we give a link between this
exponent and its Lelong number.
