Fundamental normality test

In complex analysis, a mathematical discipline, the fundamental normality test gives sufficient conditions to test the normality of a family of analytic functions. It is another name for the stronger version of Montel's theorem.

Statement

Let $ℱ$ be a family of analytic functions defined on a domain $\Omega$. If there are two fixed complex numbers a and b such that for all ƒ ∈ $ℱ$ and all x ∊ $\Omega$, f(x) ∉ {a, b}, then $ℱ$ is a normal family on $\Omega$.

The proof relies on properties of the elliptic modular function and can be found here:

See also

• Montel's theorem