caa a22 4500 445868686 CHVBK 20180317145505.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s00605-010-0213-0 doi (NATIONALLICENCE)springer-10.1007/s00605-010-0213-0 Cantor series constructions contrasting two notions of normality [Elektronische Daten] [C. Altomare, B. Mance] Rényi (Mat Lapok 7:77-100, 1956) made a definition that gives a generalization of simple normality in the context of Q-Cantor series. In Mance http://arxiv.org/abs/0911.1485), 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 Lafer (Normal numbers with respect to Cantor series representation, 1974) and S̆alát (Czechoslovak Math J 18(93):476-488, 1968). Specifically, while the non-equivalence of these two notions is implicit in Lafer (Normal numbers with respect to Cantor series representation. Washington State University, 1974), in this paper, we give an explicit construction witnessing the nontrivial direction. That is, we construct a base Q as well as a real x that is Q-normal yet not Q-distribution normal. We next approach the topic of simultaneous normality by constructing an explicit example of a base Q as well as a real x that is both Q-normal and Q-distribution normal. Springer-Verlag, 2010 Cantor series nationallicence Normal numbers nationallicence Uniform distribution nationallicence Altomare C. Department of Mathematics, The Ohio State University, 231 West 18th Avenue, 43210-1174, Columbus, OH, USA aut Mance B. Department of Mathematics, The Ohio State University, 231 West 18th Avenue, 43210-1174, Columbus, OH, USA aut Monatshefte für Mathematik Springer Vienna 164/1(2011-09-01), 1-22 0026-9255 164:1<1 2011 164 605 https://doi.org/10.1007/s00605-010-0213-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00605-010-0213-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Altomare C. Department of Mathematics, The Ohio State University, 231 West 18th Avenue, 43210-1174, Columbus, OH, USA aut NATIONALLICENCE 700 1- Mance B. Department of Mathematics, The Ohio State University, 231 West 18th Avenue, 43210-1174, Columbus, OH, USA aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer Vienna 164/1(2011-09-01), 1-22 0026-9255 164:1<1 2011 164 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer