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Typical Borel measures on [0,1](d) satisfy a multifractal formalism

Abstract : In this paper, we prove that in the Baire category sense, measures supported by the unit cube of R(d) typically satisfy a multifractal formalism. To achieve this, we compute explicitly the multifractal spectrum of such typical measures mu. This spectrum appears to be linear with slope 1, starting from 0 at exponent 0, ending at dimension d at exponent d, and it indeed coincides with the Legendre transform of the L(q)-spectrum associated with typical measures mu.
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Zoltan Buczolich, Stephane Seuret. Typical Borel measures on [0,1](d) satisfy a multifractal formalism. Nonlinearity, IOP Publishing, 2010, 23 (11), pp.2905--2918. ⟨10.1088/0951-7715/23/11/010⟩. ⟨hal-00693007⟩



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