Packing sets in Euclidean space by affine transformations

Alex Iosevich, Pertti Mattila, Eyvindur Palsson +4

For Borel subsets $\Theta \subset O(d)\times {\mathbb{R}}^d$ (the set of all rigid motions) and $E\subset {\mathbb{R}}^d$, we define \begin{align*} Θ(E):=\bigcup_{(g,z)\in Θ}(gE+z). \end{ali…