On Differentiable Functions having an Everywhere Dense set of Intervals of Constancy

Author:

Bruckner A. M.,Leonard John L.

Abstract

The Cantor function C [2; p. 213], which appears in analysis as a simple example of a continuous increasing function which is not absolutely continuous, has the following properties:(i)C is defined on [0,1], with C(0) = 0, C (l) = l;(ii)C is continuous and non-decreasing on [0,1];(iii)C is constant on each interval contiguous to the perfect Cantor set P;(iv)C fails to be constant on any open interval containing points of P;(v)The set of points at which C is non-differentiable is non-denumerable.

Publisher

Canadian Mathematical Society

Subject

General Mathematics

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. The Cantor function;Expositiones Mathematicae;2006-02

2. Differentiability through change of variables;Proceedings of the American Mathematical Society;1976

3. Derivatives;The American Mathematical Monthly;1966-04

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