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On the Hausdorff dimension of graphs of prevalent continuous functions on compact sets by Bayart, Frédéric; Heurteaux, Yanick is a scholarly article available to read on EtoBox.

What is On the Hausdorff dimension of graphs of prevalent continuous functions on compact sets about?

Let $K$ be a compact set in $\rd$ with positive Hausdorff dimension. Using a Fractional Brownian Motion, we prove that in a prevalent set of continuous functions on $K$, the Hausdorff dimension of the graph is equal to $\dim_{\mathcal H}(K)+1$. This is the largest possible value. This result generalizes a previous work due to J.M. Fraser and J.T. Hyde which was exposed in the conference {\it Fractal and Related Fields~2}. The case of $\alpha$-H\"olderian functions is also discussed.

Author

Bayart, Frédéric; Heurteaux, Yanick

Published

2011

Language

EN