Abstract
Sánchez, Viader, Paradís and Carrillo (2016) proved that there exists an increasing continuous singular function $f$ on $[0,1]$ such that the set $A_f$ of points where $f$ has a nonzero finite derivative has Hausdorff dimension 1 in each subinterval of $[0,1]$. We prove a stronger (and optimal) result showing that a set $A_f$ as above can contain any prescribed $F_{\sigma}$ null subset of $[0,1]$.
Citation
Marta Kossaczká. Luděk Zajíček. "On the Set of Points at which an Increasing Continuous Singular Function has a Nonzero Finite Derivative." Real Anal. Exchange 47 (2) 461 - 466, 2022. https://doi.org/10.14321/realanalexch.47.2.1638769133
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