Conditional measures on MV-algebras

Abstract

In recent years many papers have been written generalizing some theorems, known from the Kolmogorovian probability theory, to MV-algebras. To achieve such results, so-called product MV-algebras were introduced and, using the product, the joint probability distribution was defined. In this paper we present an approach how to define the joint distributions on MV-algebras which are not necessarily closed under product. First we construct conditional measures on a given MV-algebra. And using these conditional measures we define the joint probability distributions.