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For a fixed $1 \\leq p <\\infty$, we will show that the set $$ S_p\\doteq {f \\in L^p[0,1]: f is nowhere $L^q$, for each p<q \\leq \\infty}, $$ united with ${0}$, contains an isometric and complemented copy of $\\ell_p$. In particular, this improves a result from G. Botelho, V. F\\'avaro, D. Pellegrino, and J. B. Seoane-Sep\\'ulveda, $L_p[0,1]\\setminus \\cup_{q>p} L_q[0,1]$ is spaceable for every $p>0$, preprint, 2011., since $S_p$ turns out t"},"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":"1110.5774","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-10-26T12:27:41Z","cross_cats_sorted":[],"title_canon_sha256":"dab0fa3ac146114f5b1902729a93301b9ce51d0cba837375332179b6553db058","abstract_canon_sha256":"70cbc80cfb1e3ceb7c2194d6e60e0a1775d9e8252071b2d430ec07424cca4bdc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:11.303605Z","signature_b64":"eTgAnIlOHSD/gnuXr1jPdvi3RU0SMXJ/rvFeNOjumC5XthGOtlVvoPX4VGTDls6M5TZ254RDGe20k+3Po/T3Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1c3e9275f96d5aefaae926755d2ffb93f2833a2093be34d9540cb365b9694b8","last_reissued_at":"2026-05-18T04:10:11.302705Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:11.302705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spaceability of sets of nowhere $L^q$ functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Leonardo Pellegrini, Pedro L. Kaufmann","submitted_at":"2011-10-26T12:27:41Z","abstract_excerpt":"We say that a function $f:[0,1]\\rightarrow \\R$ is \\emph{nowhere $L^q$} if, for each nonvoid open subset $U$ of $[0,1]$, the restriction $f|_U$ is not in $L^q(U)$. For a fixed $1 \\leq p <\\infty$, we will show that the set $$ S_p\\doteq {f \\in L^p[0,1]: f is nowhere $L^q$, for each p<q \\leq \\infty}, $$ united with ${0}$, contains an isometric and complemented copy of $\\ell_p$. In particular, this improves a result from G. Botelho, V. F\\'avaro, D. Pellegrino, and J. B. 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