Montel’s theorem

Suppose that G is a region.

Theorem (Montel).

A set F of holomorphic functionsMathworldPlanetmath f:GC is normal ( if and only if F is locally bounded.

In other words a sequence of holomorphic functions {fn} has a subsequence which converges uniformly on compact subsets to a holomorphic function f:G if and only if the set {fn} is locally bounded.


  • 1 John B. Conway. . Springer-Verlag, New York, New York, 1978.
Title Montel’s theorem
Canonical name MontelsTheorem
Date of creation 2013-03-22 14:17:52
Last modified on 2013-03-22 14:17:52
Owner jirka (4157)
Last modified by jirka (4157)
Numerical id 8
Author jirka (4157)
Entry type Theorem
Classification msc 30C99
Related topic AscoliArzelaTheorem
Related topic SpaceOfAnalyticFunctions