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We investigate the existence of optimal n-quantizers for this L^r-quantization propblem, derive their stationarity properties and establish for L^p-spaces E the pathwise regularity of stationary quantizers."},"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":"math/0504236","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2005-04-12T08:43:54Z","cross_cats_sorted":[],"title_canon_sha256":"437710f356384f3bcd26be469e6cb214c483f9d09080c2fa0bc8e3e9c64f0c8f","abstract_canon_sha256":"c8d18b88c46929bd0a38365efeab358f756f98c4b04b8d5a34c38592bdd8eaab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:51.205323Z","signature_b64":"JeDcKFn+V39mK9lhtrKZ0UFomm2ecej+3HztzzzxKgc0EUep63GBwJgQPqSpDg4UFIxGtn52+NxGOC9V9/jwBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b06caa0c02a4321a4251fc7da62fdd9a4292534f9b882c1ca5510d012a5fb1fc","last_reissued_at":"2026-05-18T01:08:51.204683Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:51.204683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal quantizers for Radon random vectors in a Banach space","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Harald Luschgy, Pag\\`es Gilles (PMA), Siegried Graf (Universit\\\"at Passau)","submitted_at":"2005-04-12T08:43:54Z","abstract_excerpt":"For every integer n and evrery positive real number r > 0 and a Radon random vector X with values in a Banach space E, let e\\_{n,r}(X,E) = inf{(E (\\min\\_{a \\in \\alpha} || X-a ||^r)^{1/r}}, where the infimum is taken over all subsets \\alpha of E with card(\\alpha) <= n (n-quantizers). 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