Generic validity of the multifractal formalism

Abstract : The multifractal formalism is a formula which allows to derive the spectrum of singularities of a signal from numerically computable quantities. We study its generic validity by showing that almost every function in the sense of prevalence, is multifractal and satisfies this formalism. We also apply another notion of genericity to partially reinforce this result.
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Aurélia Fraysse. Generic validity of the multifractal formalism. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2007, 39 (2), pp.593-607. ⟨hal-00689978⟩

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