Increasing singular functions with arbitrary positive derivatives at densely lying points
Classical Analysis and ODEs
2020-03-16 v1
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.
Keywords
Cite
@article{arxiv.2003.06338,
title = {Increasing singular functions with arbitrary positive derivatives at densely lying points},
author = {Gerald Kuba},
journal= {arXiv preprint arXiv:2003.06338},
year = {2020}
}