Integral Functionals of Probability that Depend Only on Mean Values
arXiv:2301.01195
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.
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