Definition:Measure Space

Definition

A measure space is a triple $\struct {X, \Sigma, \mu}$ where:

$X$ is a set

$\Sigma$ is a $\sigma$-algebra on $X$

$\mu$ is a measure on $\Sigma$.

Thus it is a measurable space $\struct {X, \Sigma}$ with a measure.

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