On the Hausdorff Dimension of Graphs of Prevalent Continuous Functions on Compact Sets

Part of the Trends in Mathematics book series (TM)


Let K be a compact set in d 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 Fractals and Related Fields II. The case of α-Hölderian functions is also discussed.


Hausdorff Dimension Fractional Brownian Motion Multifractal Analysis Hurst Parameter Weierstrass Function 


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Laboratoire de MathématiquesClermont Université, Université Blaise PascalClermont-FerrandFrance
  2. 2.Laboratoire de MathématiquesCNRS, Complexe Scientifique des Cézeaux, UMR 6620Aubiere CedexFrance

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