Lelong number
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. It was introduced by . More generally a closed positive ("p","p") current "u" on a complex manifold has a Lelong number "n"("u","x") for each point "x" of the manifold. Similarly a plurisubharmonic function also has a Lelong number at a point. Definitions. The Lelong number of a plurisubharmonic function φ at a point "x" of C 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 C as the radius tends to zero. (Here "B"("r","x") is a ball of radius "r" centered at "x".) In other words the Lelong number is a sort of measure of the local density of "A" near "x". If "x" is not in the subvariety "A" the Lelong number is 0, and if "x" is a regular point the Lelong number is 1. It can be proved that the Lelong number ν("A","x") is always an integer. Lelong number In