Geodesic
On asymptotically monogenic bounded functions
Sbornik. Mathematics, Tome 57 (1987) no. 2, pp. 449-454 
D. S. Telyakovskii. On asymptotically monogenic bounded functions. Sbornik. Mathematics, Tome 57 (1987) no. 2, pp. 449-454. http://geodesic.mathdoc.fr/item/SM_1987_57_2_a8/
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     author = {D. S. Telyakovskii},
     title = {On asymptotically monogenic bounded functions},
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     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1987_57_2_a8/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The following theorem is proved. Theorem. Suppose that the function $f(z)$ is bounded in a region $D$ and is asymptotically monogenic at all points of $D\setminus e,$ where the set $e$ is not more than countable. Then $f(z)$ can be redefined on $e$ in such a way that it becomes holomorphic on $D$. This theorem solves positively a problem of Men'shov on holomorphicity of asymptotically monogenic bounded functions. Bibliography: 2 titles.

[1] Menshov D. E., “Ob asimptoticheskoi monogennosti”, Matem. sb., 1(43) (1936), 189–210 | Zbl

[2] Saks S., Teoriya integrala, IL, M., 1949