Limits of definable families and dilations in nilmanifolds
Limits of definable families and dilations in nilmanifolds
Let $G$ be a unipotent group and $\mathcal F=\{F_t:t\in (0,\infty)\}$ a family of subsets of $G$, with $\mathcal F$ definable in an o-minimal expansion of the real field. Given a lattice $\Gamma\subseteq G$, we study the possible Hausdorff limits of $\pi(\mathcal F)$ in $G/\Gamma$ as $t$ tends to $\infty$ (here …