IUMJ

Title: How do the typical L^q-dimensions of measures behave?

Authors: Frederic Bayart

Issue: Volume 63 (2014), Issue 3, 687-726

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 in computing these values, following $q\in\mathbb{R}$.