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Conformal Images of Borel Sets
Author(s) -
Cantón A.,
Granados A.,
Pommerenke Ch.
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303002078
Subject(s) - mathematics , unit disk , borel set , holomorphic function , conformal map , boundary (topology) , unit circle , set (abstract data type) , borel equivalence relation , borel measure , unit (ring theory) , pure mathematics , combinatorics , discrete mathematics , mathematical analysis , probability measure , mathematics education , computer science , programming language
For any holomorphic map in the unit disk, the set of radial limits at a Borel set on the unit circle is a Suslin‐analytic set. Here it is proved that, for a conformal map, this set is, in fact, Borel. As a consequence, the sets of accessible boundary points, of cut points and of transition points are Borel. In addition, it is shown that the set of end points is a G δ ‐set. 2000 Mathematics Subject Classification 28A05, 30C35.