{"paper":{"title":"Inverse problems in multifractal analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.MG","authors_text":"Julien Barral","submitted_at":"2013-11-15T16:02:16Z","abstract_excerpt":"Multifractal formalism is designed to describe the distribution at small scales of the elements of $\\mathcal M^+_c(\\R^d)$, the set of positive, finite and compactly supported Borel measures on $\\R^d$. It is valid for such a measure $\\mu$ when its Hausdorff spectrum is the upper semi-continuous function given by the concave Legendre-Fenchel transform of the free energy function $\\tau_\\mu$ associated with $\\mu$; this is the case for fundamental classes of exact dimensional measures.\n  For any function $\\tau$ candidate to be the free energy function of some $\\mu\\in \\mathcal M^+_c(\\R^d)$, we build"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3895","kind":"arxiv","version":3},"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"}