{"paper":{"title":"On a representation theorem for finitely exchangeable random vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Linglong Yuan, Svante Janson, Takis Konstantopoulos","submitted_at":"2014-10-07T15:43:33Z","abstract_excerpt":"A random vector $X=(X_1,\\ldots,X_n)$ with the $X_i$ taking values in an arbitrary measurable space $(S, \\mathscr{S})$ is exchangeable if its law is the same as that of $(X_{\\sigma(1)}, \\ldots, X_{\\sigma(n)})$ for any permutation $\\sigma$. We give an alternative and shorter proof of the representation result (Jaynes \\cite{Jay86} and Kerns and Sz\\'ekely \\cite{KS06}) stating that the law of $X$ is a mixture of product probability measures with respect to a signed mixing measure. The result is \"finitistic\" in nature meaning that it is a matter of linear algebra for finite $S$. The passing from fin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1777","kind":"arxiv","version":3},"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"}