  Using a result of Fujita on approximate Zariski decompositions and the
singular version of Demailly's holomorphic Morse inequalities as obtained by
Bonavero, we express the volume of a line bundle in terms of the absolutely
continuous parts of all the positive curvature currents on it, with a way to
pick an element among them which is most homogeneous with respect to the
volume. This enables us to introduce the volume of any pseudoeffective class on
a compact Kaehler manifold, and Fujita's theorem is then extended to this
context.
