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

  • Frédéric Bayart
  • Yanick Heurteaux
Chapter
Part of the Trends in Mathematics book series (TM)

Abstract

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.

Keywords

Hausdorff Dimension Fractional Brownian Motion Multifractal Analysis Hurst Parameter Weierstrass Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© 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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