{"paper":{"title":"A Robust Version of Convex Integral Functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","math.PR","q-fin.CP"],"primary_cat":"math.FA","authors_text":"Keita Owari","submitted_at":"2013-05-26T13:57:39Z","abstract_excerpt":"We study the pointwise supremum of convex integral functionals $\\mathcal{I}_{f,\\gamma}(\\xi)= \\sup_{Q} \\left( \\int_\\Omega f(\\omega,\\xi(\\omega))Q(d\\omega)-\\gamma(Q)\\right)$ on $L^\\infty(\\Omega,\\mathcal{F},\\mathbb{P})$ where $f:\\Omega\\times\\mathbb{R}\\rightarrow\\overline{\\mathbb{R}}$ is a proper normal convex integrand, $\\gamma$ is a proper convex function on the set of probability measures absolutely continuous w.r.t. $\\mathbb{P}$, and the supremum is taken over all such measures. We give a pair of upper and lower bounds for the conjugate of $\\mathcal{I}_{f,\\gamma}$ as direct sums of a common reg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6023","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"}