Measure space
From Maths
Before we can define Measure space we need a measurable space.
Measurable Space
Let [ilmath]X[/ilmath] be a set and [ilmath]\mathcal{A} [/ilmath] a [ilmath]\sigma[/ilmath]-algebra, then [ilmath](X,\mathcal{A})[/ilmath] is a Measurable space
Measure space
A measurable space and a function, [math]\mu:\mathcal{A}\rightarrow[0,\infty][/math] which is a measure is a measure space, that is a measure space is:
[math](X,\mathcal{A},\mu:\mathcal{A}\rightarrow[0,\infty])[/math] but recall mathematicians are lazy so we just write [math](X,\mathcal{A},\mu)[/math]
