Increasing singular functions with arbitrary positive derivatives at densely lying points

Gerald Kuba

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arXiv · 2003.06338

Increasing singular functions with arbitrary positive derivatives at densely lying points

Gerald Kuba

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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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BibTeX RIS

Gerald Kuba. 2020-03-13. Increasing singular functions with arbitrary positive derivatives at densely lying points. https://arxiv.org/abs/2003.06338

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