{"paper":{"title":"Every State on Interval Effect Algebra is Integral","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anatolij Dvure\\v{c}enskij","submitted_at":"2010-05-02T22:19:10Z","abstract_excerpt":"We show that every state on an interval effect algebra is an integral through some regular Borel probability measure defined on the Borel $\\sigma$-algebra of a compact Hausdorff simplex. This is true for every effect algebra satisfying (RDP) or for every  MV-algebra. In addition, we show that each state on an effect subalgebra of an interval effect algebra $E$ can be extended to a state on $E.$ Our method represents also every state on the set of  effect operators of a Hilbert space as an integral"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.0171","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"}