## An Application of the Universality Theorem for Tverberg Partitions

We show that, as a consequence of a remarkable new result of

Attila P\'or on universal Tverberg partitions, any large-enough set

$P$ of points in $\Re^d$ has a $(d+2)$-sized subset whose Radon point

has half-space depth at least $c_d \cdot |P|$, where $c_d \in (0, 1)$

depends only on $d$. We then give an application of this result to

computing weak $\eps$-nets by random sampling. Joint work with Nabil

Mustafa.