ON THE SET OF POINTS AT WHICH AN INCREASING CONTINUOUS SINGULAR FUNCTION HAS A NONZERO FINITE DERIVATIVE
2022
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].