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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 \mathcal{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 ∈ \mathcal{F} and all x ∊ \Omega , f(x) ∉ {a, b}, then \mathcal{F} is a normal family on \Omega .
The proof relies on properties of the elliptic modular function and can be found here:
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