Let $X$ be a compact complex manifold of complex dimension $n$, let $\chi\in H^{1,1}(X,\mathbb{R})$ be a pseudoeffective class, let $\omega>0$ be a hermitian form and let $(U_{\alpha})_{\alpha}$ be a finite covering of coordinate starshaped open sets. We denote by $MA_{\chi}$ the set of closed positive $(1,1)$-currents $\gamma\in\chi$ such that

$$-\int\limits_{U_{\alpha}}h_{\alpha}\gamma^{k}\wedge\omega^{n-k}<+\infty\,,$$

with $\gamma=i\partial\bar{\partial}h_{\alpha}$, $\sup_{U_{\alpha}}h_{\alpha}=0$ and $\gamma^{k}:=i\partial\bar{\partial}(h_{\alpha}\gamma^{k-1})$ over $U_{\alpha}$, for all $k=1,...,n-1$.