{"paper":{"title":"Asymptotic uniformity of the quantization error for Moran measures on $\\mathbb{R}^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Sanguo Zhu","submitted_at":"2018-02-11T11:18:58Z","abstract_excerpt":"Let $E$ be a Moran set on $\\mathbb{R}^1$ associated with a closed interval $J$ and two sequences $(n_k)_{k=1}^\\infty$ and $(\\mathcal{C}_k=(c_{k,j})_{j=1}^{n_k})_{k\\geq1}$. Let $\\mu$ be the infinite product measure (Moran measure) on $E$ associated with a sequence $(\\mathcal{P}_k)_{k\\geq1}$ of positive probability vectors with $\\mathcal{P}_k=(p_{k,j})_{j=1}^{n_k},k\\geq 1$. We assume that \\[ \\inf_{k\\geq1}\\min_{1\\leq j\\leq n_k}c_{k,j}>0,\\;\\inf_{k\\geq1}\\min_{1\\leq j\\leq n_k}p_{k,j}>0. \\] For every $n\\geq 1$, let $\\alpha_n$ be an $n$ optimal set in the quantization for $\\mu$ of order $r\\in(0,\\infty"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03723","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"}