Definition:Finite Measure

From ProofWiki
Jump to navigation Jump to search


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:

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