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arXiv · 1009.0639

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

Zoltán Buczolich·Stéphane Seuret
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Abstract

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 $μ$. 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 $μ$.

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Zoltán Buczolich, Stéphane Seuret. 2010-09-03. Typical Borel measures on $[0,1]d$ satisfy a multifractal formalism. https://doi.org/10.1088/0951-7715%2F23%2F11%2F010

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