Heterogeneous ubiquitous systems in ${\mathbb{R}}^d$ and Hausdorff dimension

Julien Barral, Stephane Seuret

Let $\{x\_n\}\_n\ge 0$ be a sequence of $[0,1{]}^d$, $\{\lambda \_n\}\_n\ge 0$ a sequence of positive real numbers converging to 0, and $\delta >1$. Let $\mu$ be a positive Borel measure on…