Geodesic
Boundary uniqueness theorems for meromorphic functions
Sbornik. Mathematics, Tome 61 (1988) no. 2, pp. 321-334 
Yu. V. Pomel'nikov. Boundary uniqueness theorems for meromorphic functions. Sbornik. Mathematics, Tome 61 (1988) no. 2, pp. 321-334. http://geodesic.mathdoc.fr/item/SM_1988_61_2_a3/
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     author = {Yu. V. Pomel'nikov},
     title = {Boundary uniqueness theorems for meromorphic functions},
     journal = {Sbornik. Mathematics},
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     year = {1988},
     volume = {61},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_61_2_a3/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A study is made of sets of uniqueness for the class of arbitrary meromorphic functions on the disk and for the limit values over $h$-angles (domains with zero angle on the boundary and with form determined by a function $h(x)$). The sets of uniqueness are characterized with the help of the concepts of $h$-indecomposability of $h$-regularity, introduced and studied in this article. These concepts turn out to be intermediate between measure and category. The concept of the porosity of a set served as a starting point for the definition of the property of $h$-indecomposability. The central result in this paper is the following: Theorem. Let $\mathscr F$ be the class of all meromorphic functions $f(z)$ on the unit disk. A set $E$ on the boundary of the disk is a set of uniqueness for the class $\mathscr F$ and for the limit values over $h$-angles if and only if $E$ is $h$-indecomposable. Bibliography: 13 titles.

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