The Hausdorff dimension of graphs of prevalent continuous functions

Details The Hausdorff dimension of graphs of prevalent continuous functions The Hausdorff dimension of graphs of prevalent continuous functions

2011-04-12

arxiv.org/abs/1104.2206v1

Mathematics

Metric Geometry

Scientific paper

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 $[0,1]^d$ for $d \in \mathbb{N}$ 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.

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