Measurable space

Definition

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

• [ilmath](X,\mathcal{A})[/ilmath]

Pre-measurable space

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

• [ilmath](X,\mathcal{A})[/ilmath]

See also

• Pre-measure space
• Measure space
• Measurable map