Difference between revisions of "Measure space"
From Maths
m |
m |
||
| Line 1: | Line 1: | ||
| − | Before we can define Measure space we need | + | Before we can define Measure space we need a [[Measurable space]]. |
| − | + | ||
| − | + | ||
| − | + | ||
==Measure space== | ==Measure space== | ||
| − | A | + | A [[Measurable space]] {{M|(X,\mathcal{A})}} 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 18:21, 15 March 2015
Before we can define Measure space we need a Measurable space.
Measure space
A Measurable space [ilmath](X,\mathcal{A})[/ilmath] 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]
