In Stochastic Programming, Statistics or Econometrics, one often looks for the solution of optimization problems of the following form: \begin{equation} \inf_{\theta\in\Theta} \mathbb{E}_{\mathbb{P}_{}} g(\cdot,\theta)=\inf_{\theta\in\Theta} \int_{\mathbb{R}^{q}}g(y,\theta)\mathbb{P}_{}(dy) \end{equation} where $\Theta$ is a Borel subset of $\mathbb{R}^{p}$ and $\mathbb{P}$ is a probability measure defined on $\mathbf{Y}=\mathbb{R}^{q}$ endowed with its Borel $\sigma$-field $\mathcal{B}(\mathbf{Y})$ (but more general spaces can be considered).
Quantifying uniformity of a configuration of points on a space is a topic that is receiving growing attention in computer science, physics and mathematics. The problem has interesting connections with statistics, where several tests of uniformity have been introduced.