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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)

##### MSC:
 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