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We investigate the following question: When is the cone $\\Pos(K)$ (of polynomials nonnegative on $K$) included in the closure of $M$? We give an interpretation of this inclusion with respect to representing continuous linear functionals by measures. We discuss several examples; we compute the closure of $M=\\sos$ with respect to weighted norm-$p$ "},"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":"1010.2796","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-14T00:12:33Z","cross_cats_sorted":[],"title_canon_sha256":"18d9f0992596f8ce451aae611a4b3968a9a6034fe09ecc52a33158e00cc7eaae","abstract_canon_sha256":"e7842eaf1c02b2981c4297b76147c8c33f54f917b5fb05f0082707be29a45c57"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:36.856812Z","signature_b64":"7iJI5NwZZIsLCy3adLU8wCZkrv/LcYwbD2jGjLBu77ViMkObOJ/H7mlG0rK2MPasp0tmF5pxWiLKBMz7MofFAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc7a74e1f459b4ed16ed5c58a2203919ac6b88868956375029678c5484d61a49","last_reissued_at":"2026-05-18T03:35:36.855941Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:36.855941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Moment Problem for Continuous Positive Semidefinite Linear functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ebrahim Samei, Mehdi Ghasemi, Salma Kuhlmann","submitted_at":"2010-10-14T00:12:33Z","abstract_excerpt":"Let $\\tau$ be a locally convex topology on the countable dimensional polynomial $\\reals$-algebra $\\rx:=\\reals[X_1,...,X_n]$. 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