Integral Functionals of Probability that Depend Only on Mean Values
Probability
2023-01-04 v1
Abstract
It is shown that affine functions are the only continuous real valued functions on R whose integrals with respect to compactly supported probability measures depend only on the mean value of the measure.
Cite
@article{arxiv.2301.01195,
title = {Integral Functionals of Probability that Depend Only on Mean Values},
author = {Daniel W. Stroock},
journal= {arXiv preprint arXiv:2301.01195},
year = {2023}
}
Comments
This little note is my answer to question posed to me by Andrew Lyasoff who asked that I post it. I do not claim that this result is not already known