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

2018/10/31 by Made Tantrawan, Denny H. Leung · 1 citation
Economics, Econometrics and Finance · Mathematics · #Absolutely convex set #Advanced Banach Space Theory #Convex analysis #Convex set #Dual space #Fixed Point Theorems Analysis #Functional Equations Stability Results #Invariant (physics) #Order (exchange) #Quasiconvex function #Regular polygon #Subderivative #math.FA #msc:46A20 #msc:46A55 #msc:46E30 #q-fin.RM

paper · pdf · doi:10.1007/s00013-019-01398-3

published as Archiv der Mathematik. Published online on 16 November 2019 · 10 pages

openalex publication_date 2019/11/16 · openalex created_date 2019/11/22 · arxiv created 2019/12/19 · arxiv updated 2019/12/20 · openalex updated_date 2026/08/05

Abstract

This paper presents relations between several types of closedness of a law-invariant convex set in a rearrangement invariant space X. In particular, we show that order closedness, σ(X,X_n^∼)-closedness and σ(X,L^∞)-closedness of a law-invariant convex set in X are equivalent, where X_n^∼ is the order continuous dual of X. We also provide some application to proper quasiconvex law-invariant functionals with the Fatou property.

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