\begin{definition}[Definition:Discrete Measure]
Let $\struct {X, \Sigma, \mu}$ be a measure space.
Then $\mu$ is said to be a '''discrete measure''' {{iff}} it is a series of Dirac measures.
That is, {{iff}} there exist:
:a sequence $\sequence {x_n}_{n \mathop \in \N}$ in $X$
and:
:a sequence $\sequence {\lambda_n}_{n \mathop \in \N}$ in $\R$
such that:
:$(1):\quad \forall E \in \Sigma: \map \mu E = \ds \sum_{n \mathop \in \N} \lambda_n \, \map {\delta_{x_n} } E$
where $\delta_{x_n}$ denotes the Dirac measure at $x_n$.
By Series of Measures is Measure, defining $\mu$ by $(1)$ yields a measure.
\end{definition}