Category:Dirac Measure

This category contains results about 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.