Corollary 4.3. Assuming that:

$E \subset ℤ^{n}$
$A$ a family of subsets of $[n]$ such that every $i \in [n]$ is contained at least $r$ sets $A \in A$

Then

| E | \leq \prod_{A \in A} | P_{A} E |^{\frac{1}{r}} .