{"paper":{"title":"Infinite-step nilsystems, independence and complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"A. Maass, P.D. Dong, S. Donoso, S. Shao, X.D. Ye","submitted_at":"2011-05-18T10:29:19Z","abstract_excerpt":"An $\\infty$-step nilsystem is an inverse limit of minimal nilsystems. In this article is shown that a minimal distal system is an $\\infty$-step nilsystem if and only if it has no nontrivial pairs with arbitrarily long finite IP-independence sets. Moreover, it is proved that any minimal system without nontrivial pairs with arbitrarily long finite IP-independence sets is an almost one to one extension of its maximal $\\infty$-step nilfactor, and each invariant ergodic measure is isomorphic (in the measurable sense) to the Haar measure on some $\\infty$-step nilsystem. The question if such a system"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3584","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"}