{"paper":{"title":"A note on Borel--Cantelli lemmas for non-uniformly hyperbolic dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"M. Nicol, N. Haydn, S. Vaienti, T. Persson","submitted_at":"2011-03-10T19:55:03Z","abstract_excerpt":"Let $(B_{i})$ be a sequence of measurable sets in a probability space $(X,\\mathcal{B}, \\mu)$ such that $\\sum_{n=1}^{\\infty} \\mu (B_{i}) = \\infty$. The classical Borel-Cantelli lemma states that if the sets $B_{i}$ are independent, then $\\mu (\\{x \\in X : x \\in B_{i} \\text{infinitely often (i.o.)}) = 1$. Suppose $(T,X,\\mu)$ is a dynamical system and $(B_i)$ is a sequence of sets in $X$. We consider whether $T^i x\\in B_i$ for $\\mu$ a.e.\\ $x\\in X$ and if so, is there an asymptotic estimate on the rate of entry. If $T^i x\\in B_i$ infinitely often for $\\mu$ a.e.\\ $x$ we call the sequence $B_i$ a Bor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2113","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}