{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6JADUN7PRWQMARH77LROKY2R7K","short_pith_number":"pith:6JADUN7P","schema_version":"1.0","canonical_sha256":"f2403a37ef8da0c044fffae2e56351fa9989909404607eec3cbe57d0fb002f02","source":{"kind":"arxiv","id":"1502.05248","version":1},"attestation_state":"computed","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 $1\\le mm$. 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 $0m$. 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