{"paper":{"title":"Hausdorff measure of escaping and Julia sets for bounded type functions of finite order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"J\\\"orn Peter","submitted_at":"2011-02-24T09:08:20Z","abstract_excerpt":"We show that the escaping sets and the Julia sets of bounded type transcendental entire functions of order $\\rho$ become 'smaller' as $\\rho\\to\\infty$. More precisely, their Hausdorff measures are infinite with respect to the gauge function $h_\\gamma(t)=t^2g(1/t)^\\gamma$, where $g$ is the inverse of a linearizer of some exponential map and $\\gamma\\geq(\\log\\rho(f)+K_1)/c$, but for $\\rho$ large enough, there exists a function $f_\\rho$ of bounded type with order $\\rho$ such that the Hausdorff measures of the escaping set and the Julia set of $f_\\rho$ with respect to $h_{\\gamma'}$ are zero whenever"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4933","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"}