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Dynamical Borel–Cantelli lemma for recurrence theory
Published online by Cambridge University Press: 12 April 2021
Abstract
We study the dynamical Borel–Cantelli lemma for recurrence sets in a measure-preserving dynamical system
$(X, \mu , T)$
with a compatible metric d. We prove that under some regularity conditions, the
$\mu $
-measure of the following set
$\psi :\mathbb {N}\to \mathbb {R}^+$
. The applications of our main theorem include the Gauss map,
$\beta $
-transformation and homogeneous self-similar sets.
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- © The Author(s), 2021. Published by Cambridge University Press
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