{"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. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5774","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"}