{"paper":{"title":"On the Hausdorff and packing measures of slices of dynamically defined sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ariel Rapaport","submitted_at":"2015-02-18T14:26:46Z","abstract_excerpt":"Let $1\\le m<n$ be integers, and let $K\\subset\\mathbb{R}^{n}$ be a self-similar set satisfying the strong separation condition, and with $\\dim K=s>m$. We study the a.s. values of the $s-m$-dimensional Hausdorff and packing measures of $K\\cap V$, where $V$ is a typical $n-m$-dimensional affine subspace. For $0<\\rho<\\frac{1}{2}$ let $C_{\\rho}\\subset[0,1]$ be the attractor of the IFS $\\{f_{\\rho,1},f_{\\rho,2}\\}$, where $f_{\\rho,1}(t)=\\rho\\cdot t$ and $f_{\\rho,2}(t)=\\rho\\cdot t+1-\\rho$ for each $t\\in\\mathbb{R}$. We show that for certain numbers $0<a,b<\\frac{1}{2}$, for instance $a=\\frac{1}{4}$ and $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05248","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"}