{"paper":{"title":"On differentiation of integrals in Lebesgue spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dariusz Kosz, Luz Roncal, Marco Fraccaroli","submitted_at":"2025-05-08T17:13:43Z","abstract_excerpt":"We study the problem of differentiation of integrals for certain bases in the infinite-dimensional torus $\\mathbb{T}^\\omega$. In particular, for every $p_0 \\in [1,\\infty)$, we construct a basis $\\mathcal{B}$ which differentiates $L^p(\\mathbb{T}^\\omega)$ if and only if $p \\geq p_0$, thus reproving classical theorems of Hayes in $\\mathbb{R}$. The main novelty is that our $\\mathcal{B}$ is a Busemann--Feller basis consisting of rectangles (of arbitrarily large dimensions) with sides parallel to the coordinate axes. Our construction gives us the opportunity to classify all possible ranges of differ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.05425","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.05425/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}