Measurable space

Definition

A measurable space is a tuple consisting of a set $X$ and a $\sigma$-algebra $\mathcal{A}$, which we denote:

• $(X,\mathcal{A})$

Pre-measurable space

A pre-measurable space is a set $X$ coupled with an algebra, $\mathcal{A}$ (where $\mathcal{A}$ is NOT a $\sigma$-algebra) which we denote as follows:

• $(X,\mathcal{A})$

See also

• Pre-measure space
• Measure space
• Measurable map