A Borel-Cantelli lemma for intermittent interval maps

We consider intermittent maps T of the interval, with an absolutely continuous invariant probability measure μ. Kim showed that there exists a sequence of intervals An such that ∑ μ(An) = ∞, but {An} does not satisfy the dynamical Borel–Cantelli lemma, i.e. for almost every x, the set {n : T (x) ∈ An} is finite. If ∑ Leb(An) = ∞, we prove that {An} satisfies the Borel–Cantelli lemma. Our results apply in particular to some maps T whose correlations are not summable. Mathematics Subject Classification: 37A25, 37C30, 37E05