## Measurable function

### Set

context | $ \langle X,\Sigma_X\rangle\in \mathrm{MeasurableSpace}(X) $ |

context | $ \langle Y,\Sigma_Y\rangle\in \mathrm{MeasurableSpace}(Y) $ |

postulate | $ f\in \mathrm{Measurable}(X,Y) $ |

context | $ f:X\to Y $ |

$y\in \Sigma_Y$ | |

postulate | $ 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

### Parents

#### Subset of

#### Context