{"paper":{"title":"Generalized Lebesgue points for Haj{\\l} asz functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Toni Heikkinen","submitted_at":"2018-11-09T12:00:30Z","abstract_excerpt":"Let $X$ be a quasi-Banach function space over a doubling metric measure space $\\mathcal P$. Denote by $\\alpha_X$ the generalized upper Boyd index of $X$. We show that if $\\alpha_X<\\infty$ and $X$ has absolutely continuous quasinorm, then quasievery point is a generalized Lebesgue point of a quasicontinuous Haj{\\l} asz function $u\\in\\dot M^{s,X}$. Moreover, if $\\alpha_X<(Q+s)/Q$, then quasievery point is a Lebesgue point of $u$. As an application we obtain Lebesgue type theorems for Lorentz--Haj\\l asz, Orlicz--Haj\\l asz and variable exponent Haj\\l asz functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03870","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"}