Properties of functions with monotone graphs
Classical Analysis and ODEs
2012-10-09 v1
Abstract
A metric space (X,d) is monotone if there is a linear order < on X and a constant c>0 such that d(x,y) < c d(x,z) for all x<y<z in X. Properties of continuous functions with monotone graph (considered as a planar set) are investigated. It is shown, e.g., that such a function can be almost nowhere differentiable, but must be differentiable at a dense set, and that Hausdorff dimension of the graph of such a function is 1.
Cite
@article{arxiv.1210.1952,
title = {Properties of functions with monotone graphs},
author = {Ondřej Zindulka and Michael Hrušák and Tamás Mátrai and Aleš Nekvinda and Václav Vlasák},
journal= {arXiv preprint arXiv:1210.1952},
year = {2012}
}