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 $f \in \mathcal{T}$,
$$\frac{1}{|E_n|}\sum_{(s,t)\in E_n} f(s,t) \underset{n\rightarrow+\infty}{\longrightarrow} \frac{1}{4}\int_{-1}^{1}\int_{-1}^{1} f(s,t)\,\mathrm{d}s\,\mathrm{d}t.$$