Definition:Measure Space
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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