2012/04/29 by Anatolij Dvurečenskij · 7 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Algebra and Logic #Algebra over a field #Logic, Reasoning, and Knowledge #Mathematics #Measure (data warehouse) #Observable #Physics #Pure mathematics #Quantum #Quantum mechanics #Rough Sets and Fuzzy Logic #Subalgebra #math-ph #math.MP #msc:81P10
paper · pdf · doi:10.1007/s10701-012-9689-x
published in Foundations of Physics 43(2), 210-224 (Springer Science+Business Media)
arxiv created 2012/04/29 · openalex publication_date 2012/11/07 · arxiv updated 2015/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
An observable on a quantum structure is any σ-homomorphism of quantum structures from the Borel σ-algebra of the real line into the quantum structure which is in our case a monotone σ-complete effect algebras with the Riesz Decomposition Property. We show that every observable is a smearing of a sharp observable which takes values from a Boolean σ-subalgebra of the effect algebra, and we prove that for every element of the effect algebra there is its spectral measure.