Geodesic
On sets of nonexistence of radial limits of bounded analytic functions
Sbornik. Mathematics, Tome 81 (1995) no. 2, pp. 477-485 
S. V. Kolesnikov. On sets of nonexistence of radial limits of bounded analytic functions. Sbornik. Mathematics, Tome 81 (1995) no. 2, pp. 477-485. http://geodesic.mathdoc.fr/item/SM_1995_81_2_a9/
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     author = {S. V. Kolesnikov},
     title = {On sets of nonexistence of radial limits of bounded analytic functions},
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     volume = {81},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_81_2_a9/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $f(z)$ be a function defined in the unit disc $D$: $|z|<1$; $\Gamma$ the unit circle $|z|=1$; $E(f)$ the set of points of $\Gamma$ at which $f(z)$ has no radial limits. In the paper a complete characterization is given of the sets $E(f)$ for bounded analytic functions $f$ in $D$. It is proved that for any $G_{\delta\sigma}$ set $E\subset \Gamma$ of linear measure zero there exists a function $f(z)$, bounded and analytic in $D$, such that $E(f)=E$.

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