Mathematics

In Stochastic Programming, Statistics or Econometrics, one often looks for the solution of optimization problems of the following form: $$\underset{\theta \in \mathrm{\Theta }}{inf}{\mathbb{E}}_{{\mathbb{P}}_{}}g(\cdot ,\theta )=\underset{\theta \in \mathrm{\Theta }}{inf}{\int }_{{\mathbb{R}}^q}g(y,\theta ){\mathbb{P}}_{}(dy)$$ where $\mathrm{\Theta }$ 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.