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measurable_function [2013/08/16 19:43] nikolaj |
measurable_function [2013/08/18 23:45] nikolaj |
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| | @#88DDEE: $ \langle Y,\Sigma_Y\rangle\in \mathrm{MeasurableSpace}(Y) $ | | | @#88DDEE: $ \langle Y,\Sigma_Y\rangle\in \mathrm{MeasurableSpace}(Y) $ | | ||
| - | | @#55EE55: $ f\in \mathrm{MeasurableFunction}(X,Y) $ | | + | | @#55EE55: $ f\in \mathrm{Measurable}(X,Y) $ | |
| | @#88DDEE: $ f:X\to Y $ | | | @#88DDEE: $ f:X\to Y $ | | ||
| + | | $y\in \Sigma_Y$ | | ||
| - | | @#55EE55: $ f^{-1}(\Sigma_Y)=\Sigma_X $ | | + | | @#55EE55: $ f^{-1}(y)\in\Sigma_X $ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| Line 17: | Line 18: | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Sigma-algebra|Sigma-algebra]] | Wikipedia: [[http://en.wikipedia.org/wiki/Sigma-algebra|Sigma-algebra]] | ||
| ==== Context ==== | ==== Context ==== | ||
| + | === Subset of === | ||
| + | [[Function]] | ||
| === Requirements === | === Requirements === | ||
| - | [[Measure space]] | + | [[Measurable space]] |
