Arkiv för Matematik

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

A new generalization of the Lelong number

Aron Lagerberg

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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.

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

Received: 24 August 2010
Revised: 30 June 2011
First available in Project Euclid: 31 January 2017

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2011 © Institut Mittag-Leffler


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

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