{"paper":{"title":"Pointwise convergence of multiple ergodic averages and strictly ergodic models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Song Shao, Wen Huang, Xiangdong Ye","submitted_at":"2014-06-23T14:44:55Z","abstract_excerpt":"By building some suitable strictly ergodic models, we prove that for an ergodic system $(X,\\mathcal{X},\\mu, T)$, $d\\in{\\mathbb N}$, $f_1, \\ldots, f_d \\in L^{\\infty}(\\mu)$, the averages $$\\frac{1}{N^2} \\sum_{(n,m)\\in [0,N-1]^2} f_1(T^nx)f_2(T^{n+m}x)\\ldots f_d(T^{n+(d-1)m}x) $$ converge $\\mu$ a.e.\n  Deriving some results from the construction, for distal systems we answer positively the question if the multiple ergodic averages converge a.e. That is, we show that if $(X,\\mathcal{X},\\mu, T)$ is an ergodic distal system, and $f_1, \\ldots, f_d \\in L^{\\infty}(\\mu)$, then multiple ergodic averages $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5930","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"}