A+ CATEGORY SCIENTIFIC UNIT

On the differentiability of certain saltus functions

Volume 125 / 2011

Gerald Kuba Colloquium Mathematicum 125 (2011), 15-30 MSC: 26A06, 26A30, 26A27. DOI: 10.4064/cm125-1-3

Abstract

We investigate several natural questions on the differentiability of certain strictly increasing singular functions. Furthermore, motivated by the observation that for each famous singular function $ f$ investigated in the past, $ f'(\xi )=0$ if $ f'(\xi )$ exists and is finite, we show how, for example, an increasing real function $ g$ can be constructed so that $ g'(x)=2^x$ for all rational numbers $x$ and $ g'(x)=0$ for almost all irrational numbers $x$.

Authors

  • Gerald KubaInstitute of Mathematics
    University of Natural Resources and Life Sciences
    Wien, Austria
    e-mail

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