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arXiv · 1112.1931

On the Hausdorff dimension of graphs of prevalent continuous functions on compact sets

Frédéric Bayart·Yanick Heurteaux
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Abstract

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 $α$-Hölderian functions is also discussed.

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BibTeXRIS

Frédéric Bayart, Yanick Heurteaux. 2011-12-08. On the Hausdorff dimension of graphs of prevalent continuous functions on compact sets. https://arxiv.org/abs/1112.1931

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