A geometric construction of continuous, strictly increasing singular functions
Hisashi Okamoto and Marcus Wunsch
Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 83, Number 7
(2007), 114-118.
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.
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Permanent link to this document: http://projecteuclid.org/euclid.pja/1200672011
Mathematical Reviews number (MathSciNet): MR2361422
Digital Object Identifier: doi:10.3792/pjaa.83.114
Zentralblatt MATH identifier: 1163.26303
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