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:<math>H_\varepsilon = \{z=(z_1,z_2)\in\Delta^2:|z_1|<\varepsilon\ \ \text{or}\ \ 1-\varepsilon< |z_2|\}</math>
in the two-dimensional polydisk <math>\Delta^2=\{z\in\mathbb{C}^2;|z_1|<1,|z_2|<1\}</math> where <math>0 <\varepsilon < 1</math> .
'''Theorem''' {{harvtxt|Hartogs|1906}}: any holomorphic functions <math>f</math> on <math>H_\varepsilon</math> are analytically continued to <math>\Delta^2</math> . Namely, there is a holomorphic function <math>F</math> on <math>\Delta^2</math> such that <math>F=f</math> on <math>H_\varepsilon</math> .
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