Definition:Sigma-Finite Measure

Definition
Let $\mu$ be a measure on a measurable space $\left({X, \mathcal A}\right)$.

Then $\mu$ is said to be a $\sigma$-finite (or sigma-finite) measure iff there exists an exhausting sequence $\left({A_n}\right)_{n \in \N}$ in $\mathcal A$, subject to:


 * $\forall n \in \N: \mu \left({A_n}\right) < \infty$