Let $(E_n)_{n\in\mathbb{N}}$ be a sequence of finite subsets of $[-1,1]^2$ such that, for all $(u,v)\neq(0,0)$,
$$\frac{1}{|E_n|}\sum_{(s,t)\in E_n} e_{u,v}(s,t) \underset{n\rightarrow+\infty}{\longrightarrow} 0.$$
Show that for all $a,b,c,d \in [-1,1]$ such that $a < b$ and $c < d$,
$$\frac{|E_n \cap ([a,b]\times[c,d])|}{|E_n|} \underset{n\rightarrow+\infty}{\longrightarrow} \frac{|b-a||d-c|}{4}.$$