{"paper":{"title":"The Rokhlin lemma for homeomorphisms of a Cantor set","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Anthony H. Dooley, Konstantin Medynets, Sergey Bezuglyi","submitted_at":"2004-10-23T10:20:26Z","abstract_excerpt":"For a Cantor set $X$, let $Homeo(X)$ denote the group of all homeomorphisms of $X$. The main result of this note is the following theorem. Let $T\\in Homeo(X)$ be an aperiodic homeomorphism, let $\\mu_1,\\mu_2,...,\\mu_k$ be Borel probability measures on $X$, $\\e> 0$, and $n \\ge 2$. Then there exists a clopen set $E\\subset X$ such that the sets $E,TE,..., T^{n-1}E$ are disjoint and $\\mu_i(E\\cup TE\\cup...\\cup T^{n-1}E) > 1 - \\e, i= 1,...,k$. Several corollaries of this result are given. In particular, it is proved that for any aperiodic $T\\in Homeo(X)$ the set of all homeomorphisms conjugate to $T$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0410505","kind":"arxiv","version":2},"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"}