{"paper":{"title":"A good universal weight for nonconventional ergodic averages in norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Idris Assani, Ryo Moore","submitted_at":"2015-03-30T22:13:51Z","abstract_excerpt":"We will show that the sequence appearing in the double recurrence theorem is a good universal weight for the Furstenberg averages. That is, given a system $(X, \\mathcal{F}, \\mu, T)$ and bounded functions $f_1, f_2 \\in L^\\infty(\\mu)$, there exists a set of full-measure $X_{f_1, f_2}$ in $X$ that is independent of integers $a$ and $b$ and a positive integer $k$ such that for all $x \\in X_{f_1, f_2}$ and for every other measure-preserving system $(Y, \\mathcal{G}, \\nu, S)$, and each bounded and measurable function $g_1, \\ldots, g_k \\in L^\\infty(\\nu)$, the averages \\[ \\frac{1}{N} \\sum_{n=1}^N f_1(T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08863","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"}