What non-additive integral for ensemble spaces?

TL;DR

This paper investigates suitable non-additive integrals for ensemble spaces in physics, concluding that Sugeno and Choquet integrals are not appropriate for generalizing expectation values.

Contribution

It demonstrates the unsuitability of Sugeno and Choquet integrals for ensemble spaces, guiding future research on appropriate non-additive integrals.

Findings

Sugeno and Choquet integrals are not suitable for ensemble spaces

The work connects non-additive measures to quantum and classical states

Extends previous work on non-additive measures in physics

Abstract

In a previous work we were able to define a non-additive measure that can be used to represent both classical and quantum states in physics. We further extended this idea to work on a generic space of statistical ensembles (i.e. an ensemble space) in a way that connects to Choquet theory. The question of which non-additive integral is suitable to generalize the notion of expectation value remains open. In this paper we show that the Sugeno and Choquet integrals are not suitable.