Definition:Sigma-Finite Measure/Definition 1

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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

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