Gn is pseudoconvex if and only if for any family of closed analytic discs {dα}αI in G with αIdα being a relatively compact set in G then αIdα is also a relatively compact set in G.

This is the analogue of one of the definitions of a convex set. Just replace pseudoconvex with convex and closed analytic discs with closed line segmentsPlanetmathPlanetmath.


  • 1 M. Salah Baouendi, Peter Ebenfelt, Linda Preiss Rothschild. , Princeton University Press, Princeton, New Jersey, 1999.
  • 2 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
Title Kontinuitätssatz
Canonical name Kontinuitatssatz
Date of creation 2013-03-22 15:49:15
Last modified on 2013-03-22 15:49:15
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 5
Author jirka (4157)
Entry type Theorem
Classification msc 32T05
Synonym Hartogs Kontinuitätssatz
Synonym Kontinuitatssatz