{"paper":{"title":"Closedness of convex sets in Orlicz spaces with applications to dual representation of risk measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-fin.MF","authors_text":"Denny H. Leung, Foivos Xanthos, Niushan Gao","submitted_at":"2016-10-27T14:38:56Z","abstract_excerpt":"Let $(\\Phi,\\Psi)$ be a conjugate pair of Orlicz functions. A set in the Orlicz space $L^\\Phi$ is said to be order closed if it is closed with respect to dominated convergence of sequences of functions. A well known problem arising from the theory of risk measures in financial mathematics asks whether order closedness of a convex set in $L^\\Phi$ characterizes closedness with respect to the topology $\\sigma(L^\\Phi,L^\\Psi)$. (See [26, p.3585].) In this paper, we show that for a norm bounded convex set in $L^\\Phi$, order closedness and $\\sigma(L^\\Phi,L^\\Psi)$-closedness are indeed equivalent. In g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08806","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}