JournalsrmiVol. 29, No. 1pp. 315–328

Revisiting the multifractal analysis of measures

  • Fathi Ben Nasr

    Université de Monastir, Tunisia
  • Jacques Peyrière

    Université Paris-Sud 11, Orsay, France
Revisiting the multifractal   analysis of measures cover
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Abstract

New proofs of theorems on the multifractal formalism are given. They yield results even at points qq for which Olsen’s functions b(q)b(q) and B(q)B(q) differ. Indeed, we provide an example of a measure for which the functions bb and BB differ and for which the Hausdorff dimensions of the sets XαX_\alpha (the level sets of the local Hölder exponent) are given by the Legendre transform of bb and their packing dimensions by the Legendre transform of BB.

Cite this article

Fathi Ben Nasr, Jacques Peyrière, Revisiting the multifractal analysis of measures. Rev. Mat. Iberoam. 29 (2013), no. 1, pp. 315–328

DOI 10.4171/RMI/721