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We show that $\\mu_{n}$ converges vaguely to $\\mu=\\sum_{i=1}^{\\infty} p_{i} \\delta_{\\theta_i}$ if and only if $\\mu^{(k)}_{n}=\\sum"},"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":"1610.03083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-10-10T20:25:26Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"4765a9b5cfc4d437f800bd9c7abb5fbdb8aa5b05250f7bc63a9dec9ee34bad65","abstract_canon_sha256":"68b6657e8f11263335f50e1a25bd39d55d6f1e3cd88c2a1620b77f94fadc217d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:49.650007Z","signature_b64":"C6nhGqIVNX4Ma1Zp/s/uJB8wJdauMXWIrMapa5g4+SbizGx+T4rAI/vymg6apCZwV5wegdnDch+f3FflRmujBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3db654d646ce1eef2620d25498f1311b59bdd4b0b19852f5a6df3344d6ec812","last_reissued_at":"2026-05-18T01:02:49.649599Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:49.649599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Metrizing Vague Convergence of Random Measures with Applications on Bayesian Nonparametric Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Luai Al-Labadi","submitted_at":"2016-10-10T20:25:26Z","abstract_excerpt":"This paper deals with studying vague convergence of random measures of the form $\\mu_{n}=\\sum_{i=1}^{n} p_{i,n} \\delta_{\\theta_i}$, where $(\\theta_i)_{1\\le i \\le n}$ is a sequence of independent and identically distributed random variables with common distribution $\\Pi$, $(p_{i,n})_{1 \\le i \\le n}$ are random variables chosen according to certain procedures and are independent of $(\\theta_i)_{i \\geq 1}$ and $\\delta_{\\theta_i}$ denotes the Dirac measure at $\\theta_i$. 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