Stronger Bounds for Weak Epsilon-Nets in Higher Dimensions

Natan Rubin

Given a finite point set $P$ in ${\mathbb{R}}^d$, and $\epsilon >0$ we say that $N\subseteq {\mathbb{R}}^d$ is a weak $\epsilon$-net if it pierces every convex set $K$ with $|K\cap P|\ge \epsilon |P|$. We…