Abstract
A study is made of sets of uniqueness for the class of arbitrary meromorphic functions on the disk and for the limit values over -angles (domains with zero angle on the boundary and with form determined by a function ). The sets of uniqueness are characterized with the help of the concepts of -indecomposability of -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 -indecomposability. The central result in this paper is the following:Theorem. Let be the class of all meromorphic functions on the unit disk. A set on the boundary of the disk is a set of uniqueness for the class and for the limit values over -angles if and only if is -indecomposable.Bibliography: 13 titles.
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