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Rippon, P. J. and Stallard, G. M.
(2011).
DOI: https://doi.org/10.1090/S0002-9939-2011-10842-6
Abstract
Let be a transcendental entire function and
be a Fatou component of
. We show that if
is an escaping wandering domain of
, then most boundary points of
(in the sense of harmonic measure) are also escaping. In the other direction we show that if enough boundary points of
are escaping, then
is an escaping Fatou component. Some applications of these results are given; for example, if
is the escaping set of
, then
is connected.