{"paper":{"title":"On sets where $\\operatorname{lip} f$ is finite","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Bruce Hanson, Martin Rmoutil, Thomas Z\\\"urcher, Zolt\\'an Buczolich","submitted_at":"2017-08-28T07:33:25Z","abstract_excerpt":"Given a function $f\\colon \\mathbb{R}\\to \\mathbb{R}$, the so-called \"little lip\" function $\\operatorname{lip} f$ is defined as follows: \\begin{equation*} \\operatorname{lip}\n  f(x)=\\liminf_{r{\\scriptscriptstyle \\searrow} 0}\\sup_{|x-y|\\le r} \\frac{|f(y)-f(x)|}{r}. \\end{equation*} We show that if $f$ is continuous on $\\mathbb{R}$, then the set where $\\operatorname{lip} f$ is infinite is a countable union of a countable intersection of closed sets (that is an $F_{\\sigma \\delta}$ set). On the other hand, given a countable union of closed sets $E$, we construct a continuous function $f$ such that $\\o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08220","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"}