Ein metrischer Satz der C-Gleichverteilung
type: Item
instance of: scholarly article
title: Ein metrischer Satz der C-Gleichverteilung
zbMATH Open document ID: 0541.10043
DOI: 10.1007/BF01299147
published in: Monatshefte für Mathematik
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178175
review text: The authors establish an analog of the fundamental metric theorem of \textit{H. Davenport}, \textit{P. Erdős}, and \textit{W. J. LeVeque} [Mich. Math. J. 10, 311--314 (1963; Zbl 0119.28201)] in the context of continuously uniformly distributed (c.u.d.) functions mod 1. This leads to various interesting extensions of an earlier metric theorem of \textit{E. Hlawka} [Monatsh. Math. 74, 108--118 (1970; Zbl 0208.31304)]. For instance, if \(\alpha>0\) is given, then \(f(t^{\alpha})\) is a c.u.d. function mod 1 for almost all (in the sense of the Wiener measure) real-valued continuous functions \(f\) on \([0,\infty)\). Furthermore, \(\int^{t}_{0}f(u)\,du\) is a c.u.d. function mod 1 for almost all real-valued continuous functions \(f\) on \([0,\infty)\).
reviewed by: Harald Niederreiter
Mathematics Subject Classification ID: 11K06
zbMATH DE Number: 3859245
zbMATH Keywords: continuously uniformly distributed functions mod one
zbMATH Keywords: metric theorem
zbMATH Keywords: real-valued continuous functions
author: Wolfgang Müller
author: Rudolf Taschner
MaRDI profile type: Publication
cites work: Das Wienersche Maß einer gewissen Menge von Vektorfunktionen. (The Wiener measure on a certain set of vector functions.)
cites work: Ein metrischer Satz in der Theorie der C-Gleichverteilung
cites work: Q4192121
cites work: Q3259971
cites work: Q4767350
cites work: Some results in the probabilistic theory of asymptotic uniform distribution modulo 1
OpenAlex ID: W417417697
description: scientific article; zbMATH DE number 3859245