\begin{definition}[Definition:Dirac Measure]
Let $\struct {X, \Sigma}$ be a measurable space.
Let $x \in X$ be any point in $X$.
Then the '''Dirac measure at $x$''', denoted $\delta_x$ is the measure defined by:
:$\delta_x: \Sigma \to \overline \R, \ \map {\delta_x} E := \begin{cases}0 & \text{if } x \notin E \\ 1 & \text{if } x \in E \end{cases}$
where $\overline \R$ denotes the extended set of real numbers.
That $\delta_x$ actually is a measure is shown on Dirac Measure is Measure.
In fact, Dirac measure is a probability measure.
\end{definition}