Do law-invariant linear functionals collapse to the mean?

Published 23 Jul 2021 in math.FA | (2107.11239v2)

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.

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