  We introduce a quantity which measures the singularity of a plurisubharmonic
function f relative to another plurisubharmonic function g, at a point a. This
quantity, which we denote by $\nu_{a,g}(f)$, can be seen as a generalization of
the classical Lelong number, in a natural way. The main theorem of this article
says that the upper level sets of our generalized Lelong number, i.e. the sets
of the form $\{z: \nu_{z,g}(f) \geq c > 0 \}$, are in fact analytic sets, under
certain conditions on the weight g.
