{"paper":{"title":"Exchangeable measures for subshifts","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"H. Nakada, J. Aaronson, O. Sarig","submitted_at":"2004-06-28T16:30:22Z","abstract_excerpt":"Let $\\Om$ be a Borel subset of $S^\\Bbb N$ where $S$ is countable. A measure is called exchangeable on $\\Om$, if it is supported on $\\Om$ and is invariant under every Borel automorphism of $\\Om$ which permutes at most finitely many coordinates. De-Finetti's theorem characterizes these measures when $\\Om=S^\\Bbb N$. We apply the ergodic theory of equivalence relations to study the case $\\Om\\neq S^\\Bbb N$, and obtain versions of this theorem when $\\Om$ is a countable state Markov shift, and when $\\Om$ is the collection of beta expansions of real numbers in $[0,1]$ (a non-Markovian constraint)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0406578","kind":"arxiv","version":4},"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"}