# On Measures and Measurements: a Fibre Bundle approach to Contextuality

## TL;DR

This paper introduces a fibre bundle framework to formalize and analyze contextuality in probabilistic models, providing new mathematical tools and insights into the phenomenon.

## Contribution

It develops the concepts of measurable, probability, and sample fibre bundles to rigorously capture contextuality, offering a novel formalism and new perspectives.

## Key findings

- Formal definitions of fibre bundles for probabilistic models
- Illustrative examples demonstrating the framework
- New insights into the structure of contextuality

## Abstract

Contextuality is the failure of "local" probabilistic models to become global ones. In this paper we introduce the notions of \emph{measurable fibre bundles}, \emph{probability fibre bundles}, and \emph{sample fibre bundle} which capture and make precise the former statement. The central notions of contextuality are discussed under this formalism, examples worked out, and some new aspects pointed out.