{"paper":{"title":"On effective Birkhoff's ergodic theorem for computable actions of amenable groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Nikita Moriakov","submitted_at":"2017-01-23T12:58:00Z","abstract_excerpt":"We introduce computable actions of computable groups and prove the following versions of effective Birkhoff's ergodic theorem. Let $\\Gamma$ be a computable amenable group, then there always exists a canonically computable tempered two-sided F{\\o}lner sequence $(F_n)_{n \\geq\n  1}$ in $\\Gamma$. For a computable, measure-preserving, ergodic action of $\\Gamma$ on a Cantor space $\\{0,1\\}^{\\mathbb N}$ endowed with a computable probability measure $\\mu$, it is shown that for every bounded lower semicomputable function $f$ on $\\{0,1\\}^{\\mathbb N}$ and for every Martin-L\\\"of random $\\omega \\in \\{0,1\\}^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06365","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"}