Do law-invariant linear functionals collapse to the mean?
Functional Analysis
2021-11-15 v2
Abstract
In this note, we show that, on a wide range of rearrangement-invariant spaces, a law-invariant bounded linear functional is a scalar multiple of the expectation. We also construct a rearrangement-invariant space on which this property fails.
Cite
@article{arxiv.2107.11239,
title = {Do law-invariant linear functionals collapse to the mean?},
author = {Shengzhong Chen and Niushan Gao and Denny H. Leung and Lei Li},
journal= {arXiv preprint arXiv:2107.11239},
year = {2021}
}