Difference between revisions of "Measure space"
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Before we can define Measure space we need a [[Measurable space]]. | Before we can define Measure space we need a [[Measurable space]]. | ||
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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: | 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: | ||
Revision as of 18:22, 15 March 2015
Before we can define Measure space we need a Measurable space.
Definition
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]
