Definition:Sigma-Finite Measure/Definition 2

Definition
Let $\mu$ be a measure on a measurable space $\struct {X, \Sigma}$.

We say that $\mu$ is a $\sigma$-finite (or sigma-finite) measure there exists a sequence $\sequence {E_n}_{n \mathop \in \N}$ in $\Sigma$ such that:


 * $\ds X = \bigcup_{n \mathop = 1}^\infty E_n$

and:


 * $\map \mu {E_n} < \infty$ for each $n \in \N$.