{"paper":{"title":"$L^0$--convex compactness and random normal structure in $L^0(\\mathcal{F},B)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Erxin Zhang, George Yuan, Tiexin Guo, Yachao Wang","submitted_at":"2019-04-07T08:55:11Z","abstract_excerpt":"Let $(B,\\|\\cdot\\|)$ be a Banach space, $(\\Omega,\\mathcal{F},P)$ a probability space and $L^0(\\mathcal{F},B)$ the set of equivalence classes of strong random elements (or strongly measurable functions) from $(\\Omega,\\mathcal{F},P)$ to $(B,\\|\\cdot\\|)$. It is well known that $L^0(\\mathcal{F},B)$ becomes a complete random normed module, which has played an important role in the process of applications of random normed modules to the theory of Lebesgue--Bochner function spaces and random functional analysis. Let $V$ be a closed convex subset of $B$ and $L^0(\\mathcal{F},V)$ the set of equivalence cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03607","kind":"arxiv","version":1},"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"}