An approach to construct the singular monotone functions by using Markov chains
type: Item
instance of: scholarly article
title: An approach to construct the singular monotone functions by using Markov chains
zbMATH Open document ID: 0930.26004
author: Wen Liu
published in: Taiwanese Journal of Mathematics
publication date: 1999-04-06T00:00:00Z
review text: A nondecreasing function \(f\) is singular if it is continuous and \(f'(x) = 0\) almost everywhere with respect to the Lebesgue measure. The Cantor function is the best known example of nondecreasing singular functions. Example of strictly increasing singular functions have been constructed by many authors. See, for example, \textit{G. Freilich} [Am. Math. Mon. 80, 918-919 (1973; Zbl 0278.26010)], \textit{L. Takács} [Am. Math. Mon. 85, 35-37 (1978; Zbl 0394.26005)], \textit{F. Riesz} and \textit{B. Sz.-Nagy} [``Functional analysis'' (1956; Zbl 0070.10902)]. In this paper, the author presents a method for constructing singular monotone functions by using Markov chains. His approach is based on the strong laws of Markov chains.
reviewed by: Y. Xiao
Mathematics Subject Classification ID: 26A30
Mathematics Subject Classification ID: 60J10
zbMATH DE Number: 1234924
zbMATH Keywords: singular monotone function
zbMATH Keywords: strong law of Markov chain
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500406976
OpenAlex ID: W4249133028
DOI: 10.11650/TWJM/1500406976
description: scientific article; zbMATH DE number 1234924