Probability on MV algebras

Abstract

In this chapter we shall study a generalization of the model expounded in the previous chapter. We introduced a basic example, at the beginning of Section 8.1. We considered there the family of all measurable functions f: (Ω, ℒ) → [0, 1] with two binary operations (denote them by ⊕ and ⊙), a unary operation * and two fixed elements 0_Ω, 1_Ω where

$$ f \oplus g = (f + g) \wedge 1$$

$$ f \odot g = (f + g - 1) \vee 0$$

$${f^*} = 1 - f]$$