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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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.

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

First available in Project Euclid: 18 January 2008

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Primary: 26A

Continuous, monotonically increasing function singular functions


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.

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