Convergence in capacity and applications - Hiep, Pham Hoang (Mathematica Scandinavica, 2010)
In this article we prove that if $u_j, v_j, w\in\mathcal{E}(Ω)$ such that $u_j,v_j≥ w$, $\forall\ j≥ 1$, and $|u_j-v_j|→ 0$ in $C_n$-capacity, then $\lim_{j→∞}h(φ_1,…,φ_m) [(dd^cu_j)^n-(dd^cv_j)^n]=0$ in the weak-topology of measures for all $φ_1,… ,φ_m\in{\operatorname{PSH}}\cap L_{\operatorname {loc}}^∞ (Ω)$, $h\in C(\mathsf{R}^m)$. We shall then use this result to give some applications.