{"paper":{"title":"Typical Borel measures on $[0,1]d$ satisfy a multifractal formalism","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"St\\'ephane Seuret, Zolt\\'an Buczolich","submitted_at":"2010-09-03T11:51:50Z","abstract_excerpt":"In this article, we prove that in the Baire category sense, measures supported by the unit cube of $\\R^d$ typically satisfy a multifractal formalism. To achieve this, we compute explicitly the multifractal spectrum of such typical measures $\\mu$. This spectrum appears to be linear with slope 1, starting from 0 at exponent 0, ending at dimension $d$ at exponent $d$, and it indeed coincides with the Legendre transform of the $L^q$-spectrum associated with typical measures $\\mu$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0639","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"}