{"paper":{"title":"Diagonals of separately absolutely continuous mappings and their analogues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Oleksandr Sobchuk, Olena Karlova, Volodymyr Mykhaylyuk","submitted_at":"2015-12-23T14:04:23Z","abstract_excerpt":"We prove that, for an interval $X\\subseteq \\mathbb R$ and a normed space $Z$ diagonals of separately absolute continuous mappings $f:X^2\\to Z$ are exactly such mappings \\mbox{$g:X\\to Z$} that there is a sequence $(g_n)_{n=1}^{\\infty}$ of continuous mappings $g_n:X\\to Z$ with $\\lim\\limits_{n\\to\\infty}g_n(x)=g(x)$ and \\mbox{$\\sum\\limits_{n=1}^{\\infty}\\|g_{n+1}(x)-g_n(x)\\|<\\infty$} for every $x\\in X$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07475","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"}