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 if and only if 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

• Results about $\sigma$-finite measures can be found here.

Sources

• 2005: René L. Schilling: Measures, Integrals and Martingales ... (previous) ... (next): $4.2$