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arXiv · 1810.10374

On closedness of law-invariant convex sets in rearrangement invariant spaces

Made Tantrawan·Denny H. Leung
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Abstract

This paper presents relations between several types of closedness of a law-invariant convex set in a rearrangement invariant space $\mathcal{X}$. In particular, we show that order closedness, $\sigma(\mathcal{X},\mathcal{X}_n^\sim)$-closedness and $\sigma(\mathcal{X},L^\infty)$-closedness of a law-invariant convex set in $\mathcal{X}$ are equivalent, where $\mathcal{X}_n^\sim$ is the order continuous dual of $\mathcal{X}$. We also provide some application to proper quasiconvex law-invariant functionals with the Fatou property.

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Made Tantrawan, Denny H. Leung. 2018-10-24. On closedness of law-invariant convex sets in rearrangement invariant spaces. https://doi.org/10.1007/s00013-019-01398-3

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