CONVERGENCE IN CAPACITY AND APPLICATIONS

In this article we prove that if uj, vj, w ∈ E(Ω) such that uj, vj ≥ w, ∀ j ≥ 1, and |uj - vj| → 0 in Cn-capacity, then limj→∞ h(φ1,..., φm) [(ddc uj)n - (ddc vj)n] = 0 in the weak-topology of measures for all ${\mathrm{\phi }}_{1},\mathrm{...},{\mathrm{\phi }}_{\mathrm{m}}\in \mathrm{P}\mathrm{S}\mathrm{H}\cap {\mathrm{L}}_{\mathrm{l}\mathrm{o}\mathrm{c}}^{\mathrm{\infty }}\left(\mathrm{\Omega }\right)$, h ∈ C(Rm). We shall then use this result to give some applications.