Differences
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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 === | ||
- | [[Measurable space]] |