In mathematics, the Lelong number is an invariant of a point of a complex analytic variety that in some sense measures the local density at that point.
Similarly a plurisubharmonic function also has a Lelong number at a point.
The Lelong number of a plurisubharmonic function φ at a point x of Cn is For a point x of an analytic subset A of pure dimension k, the Lelong number ν(A,x) is the limit of the ratio of the areas of A ∩ B(r,x) and a ball of radius r in Ck as the radius tends to zero.
In other words the Lelong number is a sort of measure of the local density of A near x.
It can be proved that the Lelong number ν(A,x) is always an integer.