How behave the typical L^q-dimensions of measures?
classification
🧮 math.CA
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mathbbcomputedimensiontypicalbehavecompactcontaineddefinitions
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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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