The Hausdorff dimension of graphs of prevalent continuous functions
Metric Geometry
2013-07-26 v1 Probability
Abstract
We prove that the Hausdorff dimension of the graph of a prevalent continuous function is 2. We also indicate how our results can be extended to the space of continuous functions on for and use this to obtain results on the `horizon problem' for fractal surfaces. We begin with a survey of previous results on the dimension of a generic continuous function.
Keywords
Cite
@article{arxiv.1104.2206,
title = {The Hausdorff dimension of graphs of prevalent continuous functions},
author = {Jonathan M. Fraser and James T. Hyde},
journal= {arXiv preprint arXiv:1104.2206},
year = {2013}
}