Behnke-Stein theorem

Theorem (Behnke-Stein).

Suppose that GkCn are domains of holomorphy such that GkGj whenever k<j. Then k=1Gk is a domain of holomorphy.

This is related to the fact that an increasing union of pseudoconvex domains is pseudoconvex and so it can be proven using that fact and the solution of the Levi problem. Though historically this theorem was in fact used to solve the Levi problem.


  • 1 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
Title Behnke-Stein theorem
Canonical name BehnkeSteinTheorem
Date of creation 2013-03-22 14:31:13
Last modified on 2013-03-22 14:31:13
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 5
Author jirka (4157)
Entry type Theorem
Classification msc 32T05
Synonym increasing union of domains of holomorphy is a domain of holomorphy