Limits of definable families and dilations in nilmanifolds

Ya'acov Peterzil, Sergei Starchenko

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 l…