We provide three simple and direct proofs of the automatic Fatou property of quasiconvex law-invariant functionals on bounded random variables. The key ingredient is Day's generalization of Hardy-Littlewood bounds to a finitely additive setting.
Revisiting the automatic Fatou property of law-invariant functionals
Felix-Benedikt Liebrich;Cosimo Munari
2025-01-01
Abstract
We provide three simple and direct proofs of the automatic Fatou property of quasiconvex law-invariant functionals on bounded random variables. The key ingredient is Day's generalization of Hardy-Littlewood bounds to a finitely additive setting.
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