On the convergence of Padé approximants in classes of holomorphic functions

In this paper it is proved that if, for any function $f$ holomorphic in a domain $D\subset\overline{\mathbf C}$ ($\infty\in D$), the sequence $\{\pi_n(f)\}_{n\in\mathbf N}$ of its diagonal Padé approximants (corresponding to the point $z=\infty$) converges to $f$ in measure in $D$, then $\operatorname{cap}(\overline{\mathbf C}\setminus D)=0$.
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