On the differentiability of certain saltus functions
Tom 125 / 2011
Colloquium Mathematicum 125 (2011), 15-30 MSC: 26A06, 26A30, 26A27. DOI: 10.4064/cm125-1-3
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 $x$.