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An exponent-$s$ dynamical Borel-Cantelli lemma and the waiting time problem
Galatolo and Kim proved that the dynamical Borel-Cantelli property for decreasing sequences of balls is tightly connected with the waiting time problem. In systems where all such sequences are Borel-Cantelli, the time needed to enter a small ball $B$ for the first time scales as $μ(B)^{-1}$, and con
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