This paper i a continuation of the first part under the same title. The author studies a joint distribution in $\sigma$-finite measures for noncompatible observables of a quantum logic defined on some system of $\sigma$-independent Boolean sub-$\sigma$-algebras of a Boolean $\sigma$-algebra. We present some necessary and sufficient conditions fot the existence of a joint distribution. In particular, it is shown that an arbitrary system of obsevables has a joint distribution in a measure iff it may be embedded into a system of compatible observables of some quantum logic. The methods used are different from those developed for finite measures. Finally, the author deals with the connection between the existence of a joint distribution and the existence of a commutator of observables, and the quantum logic of a nonseparable Hilbert space is mentioned.
@article{104275,
author = {Anatolij Dvure\v censkij},
title = {On joint distribution in quantum logics. II. Noncompatible observables},
journal = {Applications of Mathematics},
volume = {32},
year = {1987},
pages = {436-450},
zbl = {0654.03051},
mrnumber = {0916060},
language = {en},
url = {http://dml.mathdoc.fr/item/104275}
}
Dvurečenskij, Anatolij. On joint distribution in quantum logics. II. Noncompatible observables. Applications of Mathematics, Tome 32 (1987) pp. 436-450. http://gdmltest.u-ga.fr/item/104275/
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