Stochastic independence for probability MV-algebras

TL;DR

This paper establishes a framework for embedding MV-algebras into function spaces, proving key inequalities and problems, and introduces a novel approach to stochastic independence within probability MV-algebras.

Contribution

It demonstrates that any MV-algebra can be embedded into an fMV-algebra of integrable functions and addresses stochastic independence in probability MV-algebras.

Findings

MV-algebras can be embedded into fMV-algebras of integrable functions

H"older's inequality and Hausdorff moment problem are valid for MV-algebras with product

A solution for stochastic independence in probability MV-algebras is proposed

Abstract

We prove that any MV-algebra has a faithful state can be embedded in an \em{f}MV-algebra of integrable functions. As consequence, we prove H\"older's inequality and Hausdorff moment problem for MV-algebras with product and we propose a solution for the stochastic independence of probability MV-algebras.