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Measurable function
Definition
| $ \langle X,\Sigma_X\rangle\in \mathrm{MeasurableSpace}(X) $ |
| $ \langle Y,\Sigma_Y\rangle\in \mathrm{MeasurableSpace}(Y) $ |
| $ f\in \mathrm{Measurable}(X,Y) $ |
| $ f:X\to Y $ |
| $y\in \Sigma_Y$ |
| $ 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: Sigma-algebra
Context
Subset of
Requirements
