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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1811.03870","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-11-09T12:00:30Z","cross_cats_sorted":[],"title_canon_sha256":"59890aacc969d87840414d80fce0f9cac5176c8ee0cb969790e224cca85b29c7","abstract_canon_sha256":"2f2b81943161d1477c293045ae8aa659e25db38bb01386d5f629b0810b67a7c2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:11.749944Z","signature_b64":"OxhPpBci28nZ0poVZ1SxxUvZAcn5NdPej82fqQEZC8zJR+uxbvIb0VSLgD7Pq+zCi8jAxL6VtJhVXm0f0Vd2Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0659a17ce6787ccfe742ea29ba05466b6b62243d6bfd37e6b0eb3db50770f7be","last_reissued_at":"2026-05-18T00:01:11.749244Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:11.749244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $u$. 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