{"paper":{"title":"Asymptotics of the geometric mean error for in-homogeneous self-similar measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.FA","math.IT"],"primary_cat":"math.DS","authors_text":"Sanguo Zhu, Yongjian Sheng, Youming Zhou","submitted_at":"2014-10-23T06:54:52Z","abstract_excerpt":"Let $(f_i)_{i=1}^N$ be a family of contractive similitudes on $\\mathbb{R}^q$ satisfying the open set condition. Let $(p_i)_{i=0}^N$ be a probability vector with $p_i>0$ for all $i=0,1,\\ldots,N$. We study the asymptotic geometric mean errors $e_{n,0}(\\mu),n\\geq 1$, in the quantization for the in-homogeneous self-similar measure $\\mu$ associated with the condensation system $((f_i)_{i=1}^N,(p_i)_{i=0}^N,\\nu)$. We focus on the following two independent cases: (I) $\\nu$ is a self-similar measure on $\\mathbb{R}^q$ associated with $(f_i)_{i=1}^N$; (II) $\\nu$ is a self-similar measure associated with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3359","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"}