On the probability theory on product MV algebras (Q2737568)

A strong product MV-algebra is an MV-algebra \(M\) with an additional binary operation \(\cdot\) which is commutative, associative, has \(1\) as the neutral element and satisfies the following conditions: (i) \(a\cdot(b\odot\neg c)= (a\cdot b)\odot\neg(a\cdot c)\), (ii) if \(a_n\searrow 0\), \(b_n\searrow 0\), then \(a_n\cdot b_n\searrow 0\). The author studies a generalization of probability on this structure, in particular the existence of a joint observable and other tools which enable to prove generalizations of laws of large numbers, the central limit theorem, the martingale convergence theorem and the individual ergodic theorem. A recent overview of this approach can be found in [\textit{B. Riečan} and \textit{D. Mundici}: ``Probability on MV-algebras'' in: E.~Pap (ed.), Handbook of measure theory, North-Holland, Amsterdam, 869-910 (2002; Zbl 1017.28002)].NEWLINENEWLINEFor the entire collection see [Zbl 0938.00016].