{"paper":{"title":"Averages along cubes for not necessarily commuting measure preserving transformations","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Idris Assani","submitted_at":"2005-11-02T19:45:06Z","abstract_excerpt":"We study the pointwise convergence of some weighted averages linked to averages along cubes. We show that if $(X,\\mathcal{B},\\mu, T_i)$ are not necessarily commuting measure preserving systems on the same finite measure space and if $f_i,$ $1\\leq i\\leq 6$ are bounded functions then the averages\n  $$\\frac{1}{N^3}\\sum_{n, m, p=1}^N f_1(T_1^nx) f_2(T_2^mx) f_3(T_3^px) f_4(T_4^{n+m}x) f_5(T_5^{n+p}x) f_6(T_6^{m+p}x)$$\n converge almost everywhere."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0511062","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"}