Definition:Finite Measure

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

• 2005: René L. Schilling: Measures, Integrals and Martingales ... (previous) ... (next): $4.2$
• 2013: Donald L. Cohn: Measure Theory (2nd ed.) ... (previous) ... (next): $1.2$: Measures