Difference between revisions of "Measure space"
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==Measure space== | ==Measure space== | ||
| − | A measurable space and a function, <math>\mu:\mathcal{A}\rightarrow[0,\infty]</math> is a measure space, that is a measure space is: | + | A measurable space and a function, <math>\mu:\mathcal{A}\rightarrow[0,\infty]</math> which is a [[Measure|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|mathematicians are lazy]] so we just write <math>(X,\mathcal{A},\mu)</math> | <math>(X,\mathcal{A},\mu:\mathcal{A}\rightarrow[0,\infty])</math> but recall [[Mathematicians are lazy|mathematicians are lazy]] so we just write <math>(X,\mathcal{A},\mu)</math> | ||
{{Definition|Measure Theory}} | {{Definition|Measure Theory}} | ||
Revision as of 18:05, 13 March 2015
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]
