{"paper":{"title":"On closedness of convex sets in Banach lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Denny H. Leung, Made Tantrawan","submitted_at":"2018-08-21T03:11:35Z","abstract_excerpt":"Let $X$ be a Banach lattice. A well-known problem arising from the theory of risk measures asks when order closedness of a convex set in $X$ implies closedness with respect to the topology $\\sigma(X,X_n^\\sim)$, where $X_n^\\sim$ is the order continuous dual of $X$. Motivated by the solution in the Orlicz space case, we introduce two relevant properties: the disjoint order continuity property ($DOCP$) and the order subsequence splitting property ($OSSP$). We show that when $X$ is monotonically complete with $OSSP$ and $X_n^\\sim$ contains a strictly positive element, every order closed convex set"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06747","kind":"arxiv","version":2},"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"}