Singular strictly monotone functions

被引：2

作者：

Ryabinin, AA ^{[1
]}

Bystritskii, VD ^{[1
]}

Il'ichev, VA ^{[1
]}

机构：

[1] NI Lobachevskii State Univ, Nizhnii Novgorod, Russia

来源：

MATHEMATICAL NOTES | 2004年 / 76卷 / 3-4期

关键词：

singular strictly monotone function; random permutation of signs; Salem function; cylinder set; Borel space; Fourier-Stieltjes transformation;

D O I：

10.1023/B:MATN.0000043468.33152.2d

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We describe a universal approach to constructing continuous strictly monotone increasing singular functions on the closed interval [-1, 1]. The "generator" of the method is the series Sigma(k=1)(infinity) +/-2(-k) with random permutation of signs, and the corresponding functions are generated as distribution functions of such series. As examples, we consider two stochastic methods of arranging signs: independent and Markov.

引用

页码：407 / 419

页数：13

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