{"paper":{"title":"Convergence of ergodic averages for many group rotations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.GR"],"primary_cat":"math.DS","authors_text":"Gabriella Keszthelyi, Zoltan Buczolich","submitted_at":"2014-11-03T14:44:42Z","abstract_excerpt":"Suppose that G is a compact Abelian topological group, m is the Haar measure on G and f is a measurable function. Given (n_k), a strictly monotone increasing sequence of integers we consider the nonconventional ergodic/Birkhoff averages M_N^{\\alpha}f(x). The f-rotation set is Gamma_f={\\alpha \\in G: M_N^{\\alpha} f(x) converges for m a.e. x as N\\to \\infty .} We prove that if G is a compact locally connected Abelian group and f: G -> R is a measurable function then from m(Gamma_f)>0 it follows that f \\in L^1(G). A similar result is established for ordinary Birkhoff averages if G=Z_{p}, the group "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0508","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"}