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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 $T$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0410505","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2004-10-23T10:20:26Z","cross_cats_sorted":[],"title_canon_sha256":"df230f0cb1ace1a4cfb538c870db8d6ade3460981fd35bc44fcb202ea73ec92c","abstract_canon_sha256":"cbf9aeb7e30d8429f4a89c0142bedd0443ee7e74919104426911633a6e1db676"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:35.935990Z","signature_b64":"/prYHsAtBfchUk3RkPII7z6+PlnAem3liK2fLKJNBNiJGZTJgGBbfyh6f+x2gpHza/qAZzvYeCgNW59Oz6o3Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f12f154bad727fb9343d04615a771776580b549190c6a5c56d7cff01bb51744","last_reissued_at":"2026-05-18T04:08:35.935461Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:35.935461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Rokhlin lemma for homeomorphisms of a Cantor set","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Anthony H. 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