New proofs of theorems on the multifractal formalism are given. They yield results even at points for which Olsen’s functions and differ. Indeed, we provide an example of a measure for which the functions and differ and for which the Hausdorff dimensions of the sets (the level sets of the local Hölder exponent) are given by the Legendre transform of and their packing dimensions by the Legendre transform of .
Cite this article
Fathi Ben Nasr, Jacques Peyrière, Revisiting the multifractal analysis of measures. Rev. Mat. Iberoam. 29 (2013), no. 1, pp. 315–328DOI 10.4171/RMI/721