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Let $g\in A(\mathbb{D})$ (Dirichlet algebra), so $g(z)$ is analytic in $\mathbb{D}=(|z|<1)$ and continuous in $\mathbb{D}=(|z|\leq 1)$.
How is it possible to show that:
1) The family of functions $G_r(t)=|g(re^{it})|^2,\;0<r\leq1$ is equicontinuous;
2) $G_r(t)\to G_1(t)$ uniformly when $r\to1$...
