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CONFORMAL IMAGES OF BOREL SETS

Published online by Cambridge University Press:  09 June 2003

A. CANTÓN ,
A. GRANADOS  and
CH. POMMERENKE
A. CANTÓN
Affiliation:
Department of Mathematics, University of Washington, Seattle, WA 98102, USAcanton@math.washington.edu
A. GRANADOS
Affiliation:
Department of Mathematics, University of Washington, Seattle, WA 98102, USAgranados@math.washington.edu
CH. POMMERENKE
Affiliation:
Fachbereich Mathematik MA 8-2, Technische Universität, D-10623 Berlin, Germanypommeren@math.tu-berlin.de
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Abstract

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 $G_{\delta}$-set.

Keywords

28A0530C35
Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 35 , Issue 4 , July 2003 , pp. 479 - 483
Copyright
© The London Mathematical Society 2003

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