{"paper":{"title":"Observables on Quantum Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Anatolij Dvure\\v{c}enskij, M\\'aria Kukov\\'a","submitted_at":"2012-04-29T07:37:22Z","abstract_excerpt":"An observable on a quantum structure is any $\\sigma$-homomorphism of quantum structures from the Borel $\\sigma$-algebra into the quantum structure. We show that our partial information on an observable known only for all intervals of the form $(-\\infty,t)$ is sufficient to determine uniquely the whole observable defined on quantum structures like $\\sigma$-MV-algebras, $\\sigma$-effect algebras, Boolean $\\sigma$-algebras, monotone $\\sigma$-complete effect algebras with the Riesz Decomposition Property, the effect algebra of effect operators of a Hilbert space, and a system of functions, and an e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6460","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"}