{"paper":{"title":"The Egoroff Theorem for Operator-Valued Measures in Locally Convex Spaces","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"J\\'an Halu\\v{s}ka, Ondrej Hutn\\'ik","submitted_at":"2011-01-25T03:02:34Z","abstract_excerpt":"The Egoroff theorem for measurable $\\bold X$-valued functions and operator-valued measures $\\bold m: \\Sigma \\to L(\\bold X, \\bold Y)$, where $\\Sigma$ is a $\\sigma$-algebra of subsets of $T \\neq \\emptyset$ and $\\bold X$, $\\bold Y$ are both locally convex spaces, is proved. The measure is supposed to be atomic and the convergence of functions is net."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4708","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"}