{"paper":{"title":"ON a certain class of norms in semimodular spaces and their monotonicity properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Grzegorz Lewicki, Maciej Ciesielski","submitted_at":"2018-03-01T17:26:26Z","abstract_excerpt":"Let X be a linear space over K, K=R or K=C and let for n>1 \\rho_i be s-convex semimodular defined on X for any i\\in{1,...,n-1}. Put \\rho=\\max_{1\\leq i \\leq n-1}\\{\\rho_i\\} and\n  X_{\\rho}= { x \\in X: \\rho(dx) < \\infty for some d > 0 }. In this paper we define a new class of s-norms (norms if s=1) on X_{\\rho}. In particular, our defintion generalizes in a natural way the Orlicz-Amemiya and Luxemburg norms defined for s-convex semimodulars. Then, we investigate order continuous, the Fatou Property and various monotonicity properties of semimodular spaces equipped with these s-norms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00517","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"}