\begin{definition}[Definition:Measure Space]
A '''measure space''' is a triple $\struct {X, \Sigma, \mu}$ where:
:$X$ is a set
:$\Sigma$ is a $\sigma$-algebra on $X$
:$\mu$ is a measure on $\Sigma$.
Thus it is a measurable space $\struct {X, \Sigma}$ with a measure.
\end{definition}