I have the following problem about normal families:
Let $A(\Omega)$ be the set of all analytic function in $\Omega$.
Is it true that if $\{f_{n}\} _n{_\in \mathbb{_N}} ⊂ A(Ω)$ is normal, then for some sequence $\{m_{n}\} _n{_\in \mathbb{_N}}$, $ m_{n}→ ∞ $ a subsequence $\{f^{m_{n}}_{n}\} _n{_\in \mathbb{_N}} $ is normal.
I'm not sure, I think it's not true because the boundedness may not preserved...but I don't have an example or a good explanation.
Any help would be appreciated.