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measurable_function [2013/08/18 15:00] nikolaj |
measurable_function [2014/03/21 11:11] (current) |
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| ===== Measurable function ===== | ===== Measurable function ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $ \langle X,\Sigma_X\rangle\in \mathrm{MeasurableSpace}(X) $ | | + | | @#55CCEE: context | @#55CCEE: $ \langle X,\Sigma_X\rangle\in \mathrm{MeasurableSpace}(X) $ | |
| - | | @#88DDEE: $ \langle Y,\Sigma_Y\rangle\in \mathrm{MeasurableSpace}(Y) $ | | + | | @#55CCEE: context | @#55CCEE: $ \langle Y,\Sigma_Y\rangle\in \mathrm{MeasurableSpace}(Y) $ | |
| - | | @#55EE55: $ f\in \mathrm{Measurable}(X,Y) $ | | + | | @#55EE55: postulate | @#55EE55: $ f\in \mathrm{Measurable}(X,Y) $ | |
| - | | @#88DDEE: $ f:X\to Y $ | | + | | @#55CCEE: context | @#55CCEE: $ f:X\to Y $ | |
| | $y\in \Sigma_Y$ | | | $y\in \Sigma_Y$ | | ||
| - | | @#55EE55: $ f^{-1}(y)\in\Sigma_X $ | | + | | @#55EE55: postulate | @#55EE55: $ f^{-1}(y)\in\Sigma_X $ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| Line 17: | Line 17: | ||
| ==== Reference ==== | ==== Reference ==== | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Sigma-algebra|Sigma-algebra]] | Wikipedia: [[http://en.wikipedia.org/wiki/Sigma-algebra|Sigma-algebra]] | ||
| - | ==== Context ==== | + | ==== Parents ==== |
| === Subset of === | === Subset of === | ||
| [[Function]] | [[Function]] | ||
| - | === Requirements === | + | === Context === |
| - | [[Measure space]] | + | [[Measurable space]] |
