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On strong forms of the Borel--Cantelli lemma and intermittent interval maps (2101.05586v1)
Published 14 Jan 2021 in math.PR and math.DS
Abstract: We derive new variants of the quantitative Borel--Cantelli lemma and apply them to analysis of statistical properties for some dynamical systems. We consider intermittent maps of $(0,1]$ which have absolutely continuous invariant probability measures. In particular, we prove that every sequence of intervals with left endpoints uniformly separated from zero is the strong Borel--Cantelli sequence with respect to such map and invariant measure.