{"paper":{"title":"Validity space of Dunford-Schwartz pointwise ergodic theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Semyon Litvinov, Vladimir Chilin","submitted_at":"2017-05-08T16:14:16Z","abstract_excerpt":"We show that if a $\\sigma-$finite infinite measure space $(\\Omega,\\mu)$ is quasi-non-atomic, then the Dunford-Schwartz pointwise ergodic theorem holds for $f\\in \\mathcal L^1(\\Omega)+\\mathcal L^{\\infty}(\\Omega)$ if and only if $\\mu\\{f\\ge \\lambda\\}<\\infty$ for all $\\lambda>0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02947","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"}