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arXiv · 1203.2813

How behave the typical $L^q$-dimensions of measures?

Frédéric Bayart
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Abstract

We compute, for a compact set $K\subset\mathbb R^d$, the value of the upper and of the lower $L^q$-dimension of a typical probability measure with support contained in $K$, for any $q\in\mathbb R$. Different definitions of the "dimension" of $K$ are involved to compute these values, following $q\in\mathbb R$.

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Frédéric Bayart. 2012-03-13. How behave the typical $L^q$-dimensions of measures?. https://arxiv.org/abs/1203.2813

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