Revista Matemática Iberoamericana

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Volume 29, Issue 1, 2013, pp. 315–328
DOI: 10.4171/RMI/721

Published online: 2013-01-14

Revisiting the multifractal analysis of measures

Fathi Ben Nasr[1] and Jacques Peyrière[2]

(1) Université de Monastir, Tunisia
(2) Université Paris-Sud 11, Orsay, France

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

Keywords: Hausdorff dimension, packing dimension, fractal, multifractal

Ben Nasr Fathi, Peyrière Jacques: Revisiting the multifractal analysis of measures. Rev. Mat. Iberoam. 29 (2013), 315-328. doi: 10.4171/RMI/721