Do law-invariant linear functionals collapse to the mean?

Do law-invariant linear functionals collapse to the mean?

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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Bibliographische Detailangaben
Hauptverfasser: Chen, Shengzhong, Gao, Niushan, Leung, Denny H, Li, Lei
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Functional Analysis
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Beschreibung
Zusammenfassung: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.
DOI:10.48550/arxiv.2107.11239