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On the product MV algebras. (English) Zbl 0951.06013
The author defines a product on an MV-algebra \((M, \oplus ,\odot ,^*,0,1)\) as a total operation \(\cdot \) which is left and right distributive with respect to \(a \oplus b\) whenever \(a\leq b^*\), and in addition if \(a_n \searrow 0\) and \(b_n \searrow 0\), then \(a_n\cdot b_n \searrow 0\).
The main result is a construction of a product measure on a \(\sigma \)-complete weakly \(\sigma \)-distributive MV-algebra, which is applied to the construction of the joint observable.

MSC:
06D35 MV-algebras
28A35 Measures and integrals in product spaces
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
03G12 Quantum logic
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