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On the joint observable in some quantum structures. (English) Zbl 0806.28015
Let \((\Omega,S)\) be a measurable space and let \(F\) be the space of all \(S\)-measurable functions \(\Omega\to [0,1]\). On \(F\), we may define the basic quantum probability objects – states (= \(\sigma\)-additive probability measures) and observables (= \(\sigma\)-homomorphisms of the Borel \(\sigma\)-algebra to \(F\)).
The authors prove the existence of a joint observable and of the sum of two observables. The notion of independent observables is treated also for a more general structure.
Reviewer: M.Navara (Praha)

28E10 Fuzzy measure theory
03E72 Theory of fuzzy sets, etc.
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
46S40 Fuzzy functional analysis
28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence