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

2021/11/29 by Marta Kossaczka, Kossaczka, Marta, Ludek Zajicek +1
Mathematics · #26A30 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:26A30

paper · pdf · doi:10.48550/arxiv.2111.14519

4 pages

arxiv created 2021/12/07 · arxiv updated 2021/12/08

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_σ null subset of [0,1].

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