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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1512.09161","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-30T21:54:58Z","cross_cats_sorted":[],"title_canon_sha256":"f8efefef5ea1fde6fe39b1907344d943dfc36abcf7c29bd2e5652ff3f092af2b","abstract_canon_sha256":"c0eaa52ada1d53c3695acb8363b41debe0641ce5969d0f336641a9fcc41ddc2b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:55.819958Z","signature_b64":"cwK8M+FVcoVEZJz2IoxiZy/0S3XqwfwHoQ3HeuqXna/BGQgRRiotSgpr6QYYu/OI6mZ46Z73curr4zAGdyvUAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e3313064f239d85215617ab242ddb145af457250a49788ce7791847270c296f","last_reissued_at":"2026-05-18T00:07:55.819051Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:55.819051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $x\\in \\mathbb R$. 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