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measurable_function [2013/08/18 23:45]
nikolaj
measurable_function [2014/03/21 11:11]
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-===== Measurable function ===== 
-==== Definition ==== 
-| @#88DDEE: $ \langle X,​\Sigma_X\rangle\in \mathrm{MeasurableSpace}(X) $ | 
-| @#88DDEE: $ \langle Y,​\Sigma_Y\rangle\in \mathrm{MeasurableSpace}(Y) $ | 
  
-| @#55EE55: $ f\in \mathrm{Measurable}(X,​Y) $ | 
- 
-| @#88DDEE: $ f:X\to Y $ | 
-| $y\in \Sigma_Y$ | 
- 
-| @#55EE55: $ f^{-1}(y)\in\Sigma_X $ | 
- 
-==== Discussion ==== 
-This is very similar to the definition of [[continuous function]]. 
- 
-People write $f:\langle X,​\Sigma_X\rangle\to\langle Y,​\Sigma_Y\rangle$ to point out the function is measurable, although I'd say that's abuse of language. 
-==== Reference ==== 
-Wikipedia: [[http://​en.wikipedia.org/​wiki/​Sigma-algebra|Sigma-algebra]] 
-==== Context ==== 
-=== Subset of === 
-[[Function]] 
-=== Requirements === 
-[[Measureable space]] 
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