2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223198We study the complex Monge-Ampre operator on the classes of finite pluricomplex energy $\mathcal{E}_χ(Ω)$ in the general case ($χ(0)=0$ i.e. the total Monge-Ampre mass may be infinite). We establish an interpretation of these classes in terms of the speed of decrease of the capacity of sublevel sets and give a complete description of the range of the operator $(dd^c \cdot)^n$ on the classes $\mathcal{E}χ(Ω).$Contrary to what we claimed in the previous version, in Theorem 5.1 we generalize some Theorem of Urban Cegrell but we do not give a new proof. To appear in Potenial AnalysisComplex Variables32W20, 32U05, 32U15text