{"paper":{"title":"Almost uniform and strong convergences in ergodic theorems for symmetric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Semyon Litvinov, Vladimir Chilin","submitted_at":"2018-02-20T01:45:25Z","abstract_excerpt":"Let $(\\Omega,\\mu)$ be a $\\sigma$-finite measure space, and let $X\\subset L^1(\\Omega)+L^\\infty(\\Omega)$ be a fully symmetric space of measurable functions on $(\\Omega,\\mu)$. If $\\mu(\\Omega)=\\infty$, necessary and sufficient conditions are given for almost uniform convergence in $X$ (in Egorov's sense) of Ces\\`aro averages $M_n(T)(f)=\\frac1n\\sum_{k = 0}^{n-1}T^k(f)$ for all Dunford-Schwartz operators $T$ in $L^1(\\Omega)+ L^\\infty(\\Omega)$ and any $f\\in X$. Besides, it is proved that the averages $M_n(T)$ converge strongly in $X$ for each Dunford-Schwartz operator $T$ in $L^1(\\Omega)+L^\\infty(\\Om"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06932","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"}