. Let $(X,\omega)$ be a polarized compact Kähler manifold of complex dimension $n$ and let $\gamma$, $T$ be closed positive $(1,1)$-currents with continuous local potentials, let $\Theta$ be a closed positive $(n-1,n-1)$-current and consider $\varphi\in\check{\cal P}_{\gamma}$, $\varphi\leq 0$, $\psi\in{\cal P}_{\gamma}\cap C^{0}(X)$, $\psi\leq 0$. Then for all $k,l\geq 0$, $k+l\leq n-1$,

	$\displaystyle\int\limits_{X}i\partial\varphi\wedge\bar{\partial}\varphi\wedge\gamma_{\varphi}^{k}\wedge T^{l}\wedge\omega^{n-k-l-1}<+\infty\,,$		(3.14)
	$\displaystyle\int\limits_{X}i\partial\psi\wedge\bar{\partial}\psi\wedge\Theta<+\infty\,.$		(3.15)

Moreover let $(\varphi_{\varepsilon})_{\varepsilon>0}$, $(\psi_{\varepsilon})_{\varepsilon>0}\subset C^{\infty}(X)$, $\varphi_{\varepsilon}\in{\cal P}_{\gamma+R\omega}$, $\psi_{\varepsilon}\in{\cal P}_{\gamma+\varepsilon\omega}$ such that $\varphi_{\varepsilon}\downarrow\varphi$, $\psi_{\varepsilon}\downarrow\psi$ as $\varepsilon\rightarrow 0^{+}$. Then

	$\displaystyle\lim_{\varepsilon\rightarrow 0^{+}}\,\int\limits_{X}i\partial(\varphi_{\varepsilon}-\varphi)\wedge\bar{\partial}(\varphi_{\varepsilon}-\varphi)\wedge\gamma_{\varphi}^{k}\wedge T^{l}\wedge\omega^{n-k-l-1}=0\,,$		(3.16)
	$\displaystyle\lim_{\varepsilon\rightarrow 0^{+}}\,\int\limits_{X}i\partial(\psi_{\varepsilon}-\psi)\wedge\bar{\partial}(\psi_{\varepsilon}-\psi)\wedge\Theta=0\,.$		(3.17)