  Given a finite point set $P\subset\mathbb{R}^d$, we call a multiset $A$ a
one-sided weak $\varepsilon$-approximant for $P$ (with respect to convex sets),
if $|P\cap C|/|P|-|A\cap C|/|A|\leq\varepsilon$ for every convex set $C$.
  We show that, in contrast with the usual (two-sided) weak
$\varepsilon$-approximants, for every set $P\subset \mathbb{R}^d$ there exists
a one-sided weak $\varepsilon$-approximant of size bounded by a function of
$\varepsilon$ and $d$.
