# zbMATH — the first resource for mathematics

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
##### Keywords:
MV algebra; product of measures; joint observable