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On the product of semigroup valued measures. (English) Zbl 0917.28011
A version of Alexandroff’s theorem for measures defined on a ring and with values in a $$\sigma$$-complete commutative semigroup is proved. This result is applied to the existence of a product measure with values in a $$\sigma$$-distributive $$\ell$$-ring as well as to the existence of a joint observable on MV-algebras.
##### MSC:
 28B10 Group- or semigroup-valued set functions, measures and integrals 28B15 Set functions, measures and integrals with values in ordered spaces