{"paper":{"title":"Exchangeable sequences driven by an absolutely continuous random measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Luca Pratelli, Patrizia Berti, Pietro Rigo","submitted_at":"2013-07-08T11:20:00Z","abstract_excerpt":"Let $S$ be a Polish space and $(X_n:n\\geq1)$ an exchangeable sequence of $S$-valued random variables. Let $\\alpha_n(\\cdot)=P(X_{n+1}\\in \\cdot\\mid X_1,\\...,X_n)$ be the predictive measure and $\\alpha$ a random probability measure on $S$ such that $\\alpha_n\\stackrel{\\mathrm{weak}}{\\longrightarrow}\\alpha$ a.s. Two (related) problems are addressed. One is to give conditions for $\\alpha\\ll\\lambda$ a.s., where $\\lambda$ is a (nonrandom) $\\sigma$-finite Borel measure on $S$. Such conditions should concern the finite dimensional distributions $\\mathcal {L}(X_1,\\...,X_n)$, $n\\geq1$, only. The other pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2039","kind":"arxiv","version":1},"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"}