The Empirical Measure of a Configuration of N Particles

In the setting of Wasserstein Spaces, Random Vectors, Vector Fields and Symmetric Matrices in Every Dimension: Standing Notation, whose probability space $(\Omega,\mathcal{F},P)$ is not used, let $q,N\in\mathbb{N}$.

(Empirical measure)¶ For $x\in\mathbb{R}^{qN}$ the empirical measure of $x$ is

the one-particle marginal of the Dirac measure $\delta_{x}\in\mathcal{P}(\mathbb{R}^{qN})$.