Definition:Sigma-Finite Measure/Definition 1

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 an exhausting sequence $\sequence {E_n}_{n \mathop \in \N}$ in $\Sigma$ such that:


 * $\forall n \in \N: \map \mu {E_n} < \infty$

Also see

 * Equivalence of Definitions of Sigma-Finite Measure