MV-algebras and measure: some examples

TL;DR

This paper introduces a way to define MV-algebra structures on subsets of probability spaces, illustrating how geometric topology can influence algebraic properties through simple examples and comparing with Chang's example.

Contribution

It presents a novel approach to linking MV-algebra structures with geometric topology in probability spaces, supported by illustrative examples and comparison with existing models.

Findings

MV-algebra structures can be defined on subsets of probability spaces

Geometric topology influences MV-algebraic structures

Comparison with Chang's example highlights similarities and differences

Abstract

We propose in this article a definition of a MV-algebra structure on a class of subsets of some probability spaces and we work-out some examples. Our intention is to convey, by mean of the simplest possible examples, the idea that the topology of the geometric object under consideration might be reflected in the MV-algebraic structure. We also discuss an example of Chang and discuss similarities and differences with the proposed class of examples.