Difference between revisions of "Measurable map"
From Maths
(Created page with "==Definition== Let {{M|(X,\mathcal{A})}} and {{M|(X',\mathcal{A}')}} be measurable spaces Then a map <math>T:X\rightarrow X'</math> is called '''<math>\m...") |
m |
||
| Line 2: | Line 2: | ||
Let {{M|(X,\mathcal{A})}} and {{M|(X',\mathcal{A}')}} be [[Measurable space|measurable spaces]] | Let {{M|(X,\mathcal{A})}} and {{M|(X',\mathcal{A}')}} be [[Measurable space|measurable spaces]] | ||
| − | Then a map <math>T:X\rightarrow X'</math> is called '''<math>\mathcal{A}/\mathcal{A}'</math>-measurable''' if <math>T^{-1}(A')\in\mathcal{A},\ \forall A'\in\mathcal{A}'</math> | + | Then a map <math>T:X\rightarrow X'</math> is called '''<math>\mathcal{A}/\mathcal{A}'</math>-measurable''' if |
| + | |||
| + | <math>T^{-1}(A')\in\mathcal{A},\ \forall A'\in\mathcal{A}'</math> | ||
{{Definition|Measure Theory}} | {{Definition|Measure Theory}} | ||
Revision as of 15:37, 18 March 2015
Definition
Let [ilmath](X,\mathcal{A})[/ilmath] and [ilmath](X',\mathcal{A}')[/ilmath] be measurable spaces
Then a map [math]T:X\rightarrow X'[/math] is called [math]\mathcal{A}/\mathcal{A}'[/math]-measurable if
[math]T^{-1}(A')\in\mathcal{A},\ \forall A'\in\mathcal{A}'[/math]
