{"paper":{"title":"Random convex analysis (II): continuity and subdifferentiability theorems in $L^{0}$--pre--barreled random locally convex modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Shien Zhao, Tiexin Guo, Xiaolin Zeng","submitted_at":"2015-03-30T11:08:12Z","abstract_excerpt":"In this paper, we continue to study random convex analysis. First, we introduce the notion of an $L^0$--pre--barreled module. Then, we develop the theory of random duality under the framework of a random locally convex module endowed with the locally $L^0$--convex topology in order to establish a characterization for a random locally convex module to be $L^0$--pre--barreled, in particular we prove that the model space $L^{p}_{\\mathcal{F}}(\\mathcal{E})$ employed in the module approach to conditional risk measures is $L^0$--pre--barreled, which forms the most difficult part of this paper. Finall"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08637","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"}