{"paper":{"title":"Non-intersecting splitting algebras in a non-Bernoulli transformation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Steven Kalikow","submitted_at":"2011-08-29T20:00:23Z","abstract_excerpt":"Given a measure preserving transformation $T$ on a Lebesgue $\\sigma$ algebra, a complete $T$ invariant sub $\\sigma$ algebra is said to split if there is another complete $T$ invariant sub $\\sigma$ algebra on which $T$ is Bernoulli which is completely independent of the given sub $\\sigma$ algebra and such that the two sub $\\sigma$ algebras together generate the entire $\\sigma$ algebra. It is easily shown that two splitting sub $\\sigma$ algebras with nothing in common imply $T$ to be K. Here it is shown that $T$ does not have to be Bernoulli by exhibiting two such non-intersecting $\\sigma$ algeb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5737","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"}