Dirac_measure

Definition

Let $\left. \left( X,\mathcal{A} \right) \right.$ be a measurable_space and let $x \in X$ be some point. Then $\delta_{x}:\mathcal{A} \rightarrow \{ 0,1\}$, defined for $A \in \mathcal{A}$ by

$$ \delta_{x}\left. (A) \right. = \begin{cases} 0 & \mathrm{\text{if }}x \notin A \\ 1 & \mathrm{\text{if }}x \in A \end{cases} $$