{"paper":{"title":"Borel-Cantelli, zero-one laws and inhomogeneous Duffin-Schaeffer","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.DS","math.PR"],"primary_cat":"math.NT","authors_text":"Manuel Hauke, Sanju Velani, Victor Beresnevich","submitted_at":"2024-06-27T14:15:56Z","abstract_excerpt":"The most versatile version of the classical divergence Borel-Cantelli lemma shows that for any divergent sequence of events $E_n$ in a probability space satisfying a quasi-independence condition, its corresponding limsup set $E_\\infty$ has positive probability. In particular, it provides a lower bound on the probability of $E_\\infty$. In this paper we establish a new version of this classical result which guarantees, under an additional mild assumption, that the probability of $E_\\infty$ is not just positive but is one. Unlike existing optimal results, it is applicable within the setting of ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.19198","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.19198/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}