Physics – Mathematical Physics
Scientific paper
2010-09-03
Physics
Mathematical Physics
17 pages. To appear in Nonlinearity
Scientific paper
In this article, 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 $\mu$.
Buczolich Zoltan
Seuret Stephane
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