THE HAUSDORFF DIMENSION OF THE NONDIFFERENTIABILITY SET OF THE CANTOR FUNCTION IS [IN(2)/IN(3)]2

被引：24

作者：

DARST, R

机构：

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1993年 / 119卷 / 01期

关键词：

D O I：

10.2307/2159830

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main purpose of this note is to verify that the Hausdorff dimension of the set of points N* at which the Cantor function is not differentiable is [ln(2)/ln(3)]2. It is also shown that the image of N* under the Cantor function has Hausdorff dimension ln(2)/ln(3). Similar results follow for a standard class of Cantor sets of positive measure and their corresponding Cantor functions.

引用

页码：105 / 108

页数：4

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