Difference between revisions of "Measure space"
From Maths
(Created page with "Before we can define Measure space we need a measurable space. ==Measurable Space== Let {{M|X}} be a set and {{M|\mathcal{A} }} a \sigma}}-algebra, then...") |
m |
||
| Line 2: | Line 2: | ||
==Measurable Space== | ==Measurable Space== | ||
| − | Let {{M|X}} be a set and {{M|\mathcal{A} }} a [[Sigma algebra|{{ | + | Let {{M|X}} be a set and {{M|\mathcal{A} }} a [[Sigma-algebra|{{sigma|algebra}}]], then {{M|(X,\mathcal{A})}} is a ''Measurable space'' |
==Measure space== | ==Measure space== | ||
Revision as of 15:40, 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] 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]
