{"paper":{"title":"Multifractal properties of convex hulls of typical continuous functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Zoltan Buczolich","submitted_at":"2016-03-30T12:59:29Z","abstract_excerpt":"We study the singularity (multifractal) spectrum of the convex hull of the typical/generic continuous functions defined on $[0,1]^{d}$. We denote by ${\\mathbf E}_ { { \\varphi } }^{h} $ the set of points at which $ \\varphi : [0,1]^d\\to {\\mathbb R}$ has a pointwise H\\\"older exponent equal to $h$. Let $H_{f}$ be the convex hull of the graph of $f$, the concave function on the top of $H_{f}$ is denoted by $ { { \\varphi } }_{1,f}( { { \\mathbf x } })=\\max \\{y:( { { \\mathbf x } },y)\\in H_{f} \\}$ and $ { { \\varphi } }_{2,f}( { { \\mathbf x } })=\\min \\{y:( { { \\mathbf x } },y)\\in H_{f} \\}$ denotes the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.09162","kind":"arxiv","version":2},"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"}