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

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

2012-03-13

arxiv.org/abs/1203.2813v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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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