\begin{definition}[Definition:Sigma-Finite Measure]
Let $\mu$ be a measure on a measurable space $\left({X, \Sigma}\right)$.
Then $\mu$ is said to be a '''$\sigma$-finite''' (or '''sigma-finite''') '''measure''' iff there exists an exhausting sequence $\left({E_n}\right)_{n \in \N}$ in $\Sigma$, subject to:
:$\forall n \in \N: \mu \left({E_n}\right) < \infty$
\end{definition}