What non-additive integral for ensemble spaces?
arXiv:2602.01470
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.
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