{"paper":{"title":"Strictly ergodic models and the convergence of non-conventional pointwise ergodic averages","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":"2013-12-27T08:35:11Z","abstract_excerpt":"The well-known Jewett-Krieger's Theorem states that each ergodic system has a strictly ergodic model. Strengthening the model by requiring that it is strictly ergodic under some group actions, and building the connection of the new model with the convergence of pointwise non-conventional ergodic averages we prove that for an ergodic system $(X,\\X,\\mu, T)$, $d\\in\\N$, $f_1, \\ldots, f_d \\in L^{\\infty}(\\mu)$, %and any tempered F{\\rm ${\\o}$}lner sequence $F_n$ of $\\Z^2$, the averages \\begin{equation*}\n  \\frac{1}{N^2} \\sum_{(n,m)\\in F_N} f_1(T^nx)f_2(T^{n+m}x)\\ldots f_d(T^{n+(d-1)m}x) \\end{equation*"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7213","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"}