Behnke–Stein theorem

In mathematics, especially several complex variables, the Behnke–Stein theorem states that a union of an increasing sequence $G_k$ (i.e., $G_k \subset G_{k + 1}$) of domains of holomorphy is again 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.

References

This article incorporates material from Behnke-Stein theorem on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.