Measurable space

A measurable space is a pair $(X,\Sigma)$ consisting of a set $X$ and a sigma-algebra $\Sigma$ on $X$.

Measurable spaces are the domains and codomains for measurable functions ; adding a measure produces a measure space .

Examples:

• $(\mathbb R,\mathcal B(\mathbb R))$, where $\mathcal B(\mathbb R)$ is the Borel sigma-algebra on $\mathbb R$.
• $(X,\mathcal P(X))$, where $\mathcal P(X)$ is the power set of $X$.