{"paper":{"title":"Optimal quantization for the Cantor distribution generated by infinite similutudes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mrinal Kanti Roychowdhury","submitted_at":"2015-12-30T21:54:58Z","abstract_excerpt":"Let $P$ be a Borel probability measure on $\\mathbb R$ generated by an infinite system of similarity mappings $\\{S_j : j\\in \\mathbb N\\}$ such that $P=\\sum_{j=1}^\\infty \\frac 1{2^j} P\\circ S_j^{-1}$, where for each $j\\in \\mathbb N$ and $x\\in \\mathbb R$, $S_j(x)=\\frac 1{3^{j}}x+1-\\frac 1 {3^{j-1}}$. Then, the support of $P$ is the dyadic Cantor set $C$ generated by the similarity mappings $f_1, f_2 : \\mathbb R \\to \\mathbb R$ such that $f_1(x)=\\frac 13 x$ and $f_2(x)=\\frac 13 x+\\frac 23$ for all $x\\in \\mathbb R$. In this paper, using the infinite system of similarity mappings $\\{S_j : j\\in \\mathbb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09161","kind":"arxiv","version":6},"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"}