On the set of points at which an increasing continuous singular function has a nonzero finite derivative

Marta Kossaczka; Ludek Zajicek

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arXiv · 2111.14519

On the set of points at which an increasing continuous singular function has a nonzero finite derivative

Marta Kossaczka·Ludek Zajicek

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Abstract

Sanchez, Viader, Paradis 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 $[0,1]$.

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BibTeX RIS

Marta Kossaczka, Ludek Zajicek. 2021-11-29. On the set of points at which an increasing continuous singular function has a nonzero finite derivative. https://arxiv.org/abs/2111.14519

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