{"paper":{"title":"Pointwise convergence of some multiple ergodic averages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sebasti\\'an Donoso, Wenbo Sun","submitted_at":"2016-09-08T18:49:04Z","abstract_excerpt":"We show that for every ergodic system $(X,\\mu,T_1,\\ldots,T_d)$ with commuting transformations, the average \\[\\frac{1}{N^{d+1}} \\sum_{0\\leq n_1,\\ldots,n_d \\leq N-1} \\sum_{0\\leq n\\leq N-1} f_1(T_1^n \\prod_{j=1}^d T_j^{n_j}x)f_2(T_2^n \\prod_{j=1}^d T_j^{n_j}x)\\cdots f_d(T_d^n \\prod_{j=1}^d T_j^{n_j}x). \\] converges for $\\mu$-a.e. $x\\in X$ as $N\\to\\infty$. If $X$ is distal, we prove that the average \\[\\frac{1}{N}\\sum_{i=0}^{N} f_1(T_1^nx)f_2(T_2^nx)\\cdots f_d(T_d^nx) \\] converges for $\\mu$-a.e. $x\\in X$ as $N\\to\\infty$. We also establish the pointwise convergence of averages along cubical configur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02529","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"}