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 if and only if there exists a cover $\sequence {E_n}_{n \mathop \in \N}$ of $X$ 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

• 2013: Donald L. Cohn: Measure Theory (2nd ed.) ... (previous) ... (next): $1.2$: Measures