Continuous Functions that Cut the Real Axis Very Often
Classical Analysis and ODEs
2015-03-19 v3
Abstract
We consider continuous functions f : [0,1] \to R that cut the real axis at every point of a measurable set of positive measure and we construct examples where f fails to have bounded variation, and at the opposite end, where f admits derivatives of all orders.
Keywords
Cite
@article{arxiv.1108.2625,
title = {Continuous Functions that Cut the Real Axis Very Often},
author = {Omid Zabeti},
journal= {arXiv preprint arXiv:1108.2625},
year = {2015}
}
Comments
4 pages