## Arkiv för Matematik

• Ark. Mat.
• Volume 51, Number 1 (2013), 125-156.

### A new generalization of the Lelong number

Aron Lagerberg

#### Abstract

We will introduce a quantity which measures the singularity of a plurisubharmonic function φ relative to another plurisubharmonic function ψ, at a point a. We denote this quantity by νa, ψ(φ). It can be seen as a generalization of the classical Lelong number in a natural way: if ψ=(n−1)log| ⋅ −a|, where n is the dimension of the set where φ is defined, then νa, ψ(φ) coincides with the classical Lelong number of φ at the point a. 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: νz, ψ(φ)≥c} where c>0, are in fact analytic sets, provided that the weightψ satisfies some additional conditions.

#### Article information

Source
Ark. Mat., Volume 51, Number 1 (2013), 125-156.

Dates
Revised: 30 June 2011
First available in Project Euclid: 31 January 2017

https://projecteuclid.org/euclid.afm/1485907200

Digital Object Identifier
doi:10.1007/s11512-011-0158-0

Mathematical Reviews number (MathSciNet)
MR3029340

Zentralblatt MATH identifier
1293.32039

Rights

#### Citation

Lagerberg, Aron. A new generalization of the Lelong number. Ark. Mat. 51 (2013), no. 1, 125--156. doi:10.1007/s11512-011-0158-0. https://projecteuclid.org/euclid.afm/1485907200

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