Uniform convergence in probability
= Uniform convergence in probability
{title2=$\sup_{\theta\in\Theta}|Q_n(\theta)-Q(\theta)|\xrightarrow{P}0$}
Uniform convergence in <probability> means that the supremum of the absolute discrepancy on the entire index set tends to zero in <probability>. It controls evaluation at random indices in that set, unlike pointwise <convergence in probability>. On a fixed compact index set it is a special case of <uniform convergence on compacts in probability>.