  We study the complex Monge-Ampre operator on the classes of finite
pluricomplex energy $\mathcal{E}_\chi (\Omega)$ in the general case
($\chi(0)=0$ 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 $\mathcal{E}\chi(\Omega).$
