What non-additive integral for ensemble spaces?
Quantum Physics
2026-02-03 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.2602.01470,
title = {What non-additive integral for ensemble spaces?},
author = {Gabriele Carcassi and Christine A. Aidala and Tobias Thrien},
journal= {arXiv preprint arXiv:2602.01470},
year = {2026}
}
Comments
6 pages, 4 figures, prepared for the 21st International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Rome, Italy, June 15-19, 2026