Proceedings of the Japan Academy, Series A, Mathematical Sciences

A geometric construction of continuous, strictly increasing singular functions

Hisashi Okamoto and Marcus Wunsch

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Abstract

A parameterized family of continuous functions which was considered by the first author is re-visited in the case when they are monotonically increasing. We prove that the functions are not only continuous and strictly increasing but also singular, i.e., their derivatives are zero almost everywhere.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 83, Number 7 (2007), 114-118.

Dates
First available in Project Euclid: 18 January 2008

Permanent link to this document
https://projecteuclid.org/euclid.pja/1200672011

Digital Object Identifier
doi:10.3792/pjaa.83.114

Mathematical Reviews number (MathSciNet)
MR2361422

Zentralblatt MATH identifier
1163.26303

Subjects
Primary: 26A

Keywords
Continuous, monotonically increasing function singular functions

Citation

Okamoto, Hisashi; Wunsch, Marcus. A geometric construction of continuous, strictly increasing singular functions. Proc. Japan Acad. Ser. A Math. Sci. 83 (2007), no. 7, 114--118. doi:10.3792/pjaa.83.114. https://projecteuclid.org/euclid.pja/1200672011


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