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Typical Borel measures on $[0,1]d$ satisfy a multifractal formalism
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 $\mu$. 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 $\mu$.
https://hal.archives-ouvertes.fr/hal-00795546
Contributor : Stephane Seuret Connect in order to contact the contributor
Submitted on : Thursday, February 28, 2013 - 1:37:24 PM
Last modification on : Monday, April 25, 2022 - 3:03:48 PM
Contributor : Stephane Seuret Connect in order to contact the contributor
Submitted on : Thursday, February 28, 2013 - 1:37:24 PM
Last modification on : Monday, April 25, 2022 - 3:03:48 PM
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