Geodesic
On the convergence of Pad\'e approximants in classes of holomorphic functions
Sbornik. Mathematics, Tome 40 (1981) no. 2, pp. 149-155

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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 $\operatorname{cap}(\overline{\mathbf C}\setminus D)=0$. Bibliography: 8 titles. 
@article{SM_1981_40_2_a1,
     author = {E. A. Rakhmanov},
     title = {On the convergence of {Pad\'e} approximants in classes of holomorphic functions},
     journal = {Sbornik. Mathematics},
     pages = {149--155},
     publisher = {mathdoc},
     volume = {40},
     number = {2},
     year = {1981},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1981_40_2_a1/}
}
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E. A. Rakhmanov. On the convergence of Pad\'e approximants in classes of holomorphic functions. Sbornik. Mathematics, Tome 40 (1981) no. 2, pp. 149-155. http://geodesic.mathdoc.fr/item/SM_1981_40_2_a1/