. Let $(X,\omega)$ be a polarized connected compact Kähler manifold of complex dimension $n$ and let $\gamma$, $T$ be closed positive $(1,1)$-currents with continuous local potentials. Then for all $l=0,...,n$

$$C_{l}:=\sup_{\psi\in{\cal P}^{0}_{\gamma}}\;\int\limits_{X}-\psi\,T^{l}\wedge\omega^{n-l}<+\infty$$

and $\gamma_{\psi}\wedge T^{l}=T^{l}\wedge\gamma_{\psi}$ for all $\psi\in{\cal P}_{\gamma}$.