The Dirac Measure at a Point of Euclidean Space

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 $n\in\mathbb{N}$ and $x\in\mathbb{R}^{n}$.

(Dirac measure)¶ The Dirac measure at $x$ is the probability measure $\delta_{x}$ on $\mathbb{R}^{n}$ given by $\delta_{x}(B)=1$ if $x\in B$ and $\delta_{x}(B)=0$ if $x\notin B$, for $B\in\mathcal{B}(\mathbb{R}^{n})$; it is a probability measure by Dirac Measures on Euclidean Space: Probability Measure, Integrals, Push-Forwards and the Coupling of Two Dirac Measures §measure.