On a~class of exceptional sets in the theory of conformal mappings
Sbornik. Mathematics, Tome 68 (1991) no. 1, pp. 19-30

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A subset $E$ of the unit circle $\partial\mathbf D$ is called an $L$-set if there exists a function univalent in the disc $\mathbf D$ mapping $E$ to a set of zero linear measure. Metric properties of $L$-sets are studied, and related problems of the radial behavior of Bloch functions are also considered. Bibliography: 11 titles.
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     author = {N. G. Makarov},
     title = {On a~class of exceptional sets in the theory of conformal mappings},
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N. G. Makarov. On a~class of exceptional sets in the theory of conformal mappings. Sbornik. Mathematics, Tome 68 (1991) no. 1, pp. 19-30. http://geodesic.mathdoc.fr/item/SM_1991_68_1_a1/