Behnke–Stein theorem

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