Increasing singular functions with arbitrary positive derivatives at densely lying points

2020/03/13 by Gerald Kuba, Kuba, Gerald
Mathematics · #26A06 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:26A06

paper · pdf · doi:10.48550/arxiv.2003.06338

arxiv created 2020/03/13 · arxiv updated 2020/03/16

Abstract

Let A be an arbitrary countable set of reals, for example A=Q. Let g be an arbitrary mapping from A into the positive reals, for example g(a)=2^a. We show how a strictly increasing real function f can be constructed such that f'(x)=g(x) for every x in the set A and f'(x)=0 for almost all real numbers x.

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