The weak law of large numbers holds for triangular arrays satisfying certain conditions. For the iid case, under specific conditions an uniform law of large numbers also holds. Is there a similar uniform law for triangular arrays without the assumption of identical distributions (only row-wise independence)?
I think the uniform law (as it is stated in the wikipedia page) holds in the (iid) triangular array case, since the law is weak, i.e., the value $$P\left( \left\lvert \sup_{\theta \in \Theta} \left\lVert r_n^{-1} \sum_{k=1}^{r_n} f(X_{n,k},\theta) - E[f(X,\theta)] \right\rVert \right\rvert < \epsilon \right)$$ is the same whether our random variables form a (arbitrary) triangular array or not (that is, $r_n = n$ for all $n$ and $X_{n,k} = X_k$).