I want to show $f_n'\rightrightarrows f'$ on the region $\Omega$.
Let $\Omega_\delta = \{z\in\Omega:\overline{D_\delta}(z)\subset \Omega\}$. The textbook I'm reading states that it suffices to show $f_n'\rightrightarrows f'$ on $\Omega_\delta$ for all $\delta$. It looks fine at first sight, but I don't know how it actually makes sense. Can somebody help?