{"paper":{"title":"Cantor Series Constructions Contrasting Two Notions of Normality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bill Mance, Christian Altomare","submitted_at":"2009-11-23T04:30:42Z","abstract_excerpt":"A. R\\'enyi \\cite{Renyi} made a definition that gives a generalization of simple normality in the context of $Q$-Cantor series. In \\cite{Mance}, a definition of $Q$-normality was given that generalizes the notion of normality in the context of $Q$-Cantor series. In this work, we examine both $Q$-normality and $Q$-distribution normality, treated in \\cite{Laffer} and \\cite{Salat}. Specifically, while the non-equivalence of these two notions is implicit in \\cite{Laffer}, in this paper, we give an explicit construction witnessing the nontrivial direction. That is, we construct a base $Q$ as well as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4277","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"}