Weak $(1-\epsilon )$-nets for polynomial superlevel sets

Pablo González-Mazón, Alfredo Hubard, Roman Karasev

We prove that for any Borel probability measure $\mu$ on ${\mathbb{R}}^n$ there exists a set $X\subset {\mathbb{R}}^n$ of $n+1$ points such that any $n$-variate quadratic polynomial $P$ th…