Definition:Finite Measure

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Definition

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


Then $\mu$ is said to be a finite measure if and only if:

$\map \mu X < \infty$


Signed Measure

Let $\struct {X, \Sigma}$ be a measurable space.

Let $\mu$ be a signed measure on $\struct {X, \Sigma}$.


We say that $\mu$ is a finite signed measure if and only if:

$\size {\map \mu X} < \infty$


Sources