  We present a simple sublinear time algorithm for testing the following
geometric property. Let $P_1, ..., P_n$ be $n$ convex sets in $\mathbb{R}^d$
($n \gg d$), such as polytopes, balls, etc. We assume that the complexity of
each set depends only on $d$ (and not on the number of sets $n$). We test the
property that there exists a common point in all sets, i.e. that their
intersection is nonempty. Our goal is to distinguish between the case where the
intersection is nonempty, and the case where even after removing many of the
sets the intersection is empty. In particular, our algorithm returns PASS if
all of the $n$ sets intersect, and returns FAIL with probability at least
$1-\epsilon$ if no point belongs to $\frac{\alpha}{d+1} n$ sets, for any given
$0 < \alpha, \epsilon < 1$.
