Let $\xi_{tn}(\theta),t=1,\dots,n$ be a real-valued martingale difference array indexed by a parameter $\theta \in \Theta \subset R$, where the set $\Theta$ is compact. Now, for all fixed $\theta \in \Theta$, the law of large numbers,

$\sum_{t=1}^n \xi_{tn} (\theta) \rightarrow 0$ in probability,

is assumed to hold. Then, what conditions make the following UNIFORM law of large numbers hold?

$\sup_{\theta \in \Theta} | \sum_{t=1}^n \xi_{tn}(\theta) | \rightarrow 0$ in probability.

Are there any articles or books about the result?