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On joint distribution in quantum logics. I. Compatible observables
Applications of Mathematics, Tome 32 (1987) no. 6, pp. 427-435
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The notion of a joint distribution in $\sigma$-finite measures of observables of a quantum logic defined on some system of $\sigma$-independent Boolean sub-$\sigma$-algebras of a Boolean $\sigma$-algebra is studied. In the present first part of the paper the author studies a joint distribution of compatible observables. It is shown that it may exists, although a joint obsevable of compatible observables need not exist.
The notion of a joint distribution in $\sigma$-finite measures of observables of a quantum logic defined on some system of $\sigma$-independent Boolean sub-$\sigma$-algebras of a Boolean $\sigma$-algebra is studied. In the present first part of the paper the author studies a joint distribution of compatible observables. It is shown that it may exists, although a joint obsevable of compatible observables need not exist.
DOI : 10.21136/AM.1987.104274
Classification : 03G12, 28A60, 81B10, 81P10
Keywords: compatibility; orthomodular poset; observables; joint distribution; measure; quantum logic 
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     title = {On joint distribution in quantum logics. {I.} {Compatible} observables},
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Dvurečenskij, Anatolij. On joint distribution in quantum logics. I. Compatible observables. Applications of Mathematics, Tome 32 (1987) no. 6, pp. 427-435. doi: 10.21136/AM.1987.104274

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