{"paper":{"title":"On $d$--$\\sigma$--stability in random metric spaces and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Bixuan Yang, Erxin Zhang, Tiexin Guo, Yachao Wang","submitted_at":"2019-04-16T02:15:18Z","abstract_excerpt":"In 2010, the first author of this paper introduced the notion of $\\sigma$--stability for a nonempty subset of an $L^0(\\mathcal{F},K)$--module in [T.X. Guo, Relations between some basic results derived from two kinds of topologies for a random locally convex module, J. Funct. Anal. 258(2010), 3024--3047], this kind of $\\sigma$--stability is purely algebraic and leads to a series of deep developments of random normed modules and random locally convex modules. Motivated by this, A. Jamneshan, M. Kupper and J. M. Zapata recently introduced another kind of $\\sigma$--stability for a nonempty subset "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07405","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"}