===== Measurable function =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $ \langle X,\Sigma_X\rangle\in \mathrm{MeasurableSpace}(X) $ |
| @#55CCEE: context     | @#55CCEE: $ \langle Y,\Sigma_Y\rangle\in \mathrm{MeasurableSpace}(Y) $ |

| @#55EE55: postulate   | @#55EE55: $ f\in \mathrm{Measurable}(X,Y) $ |

| @#55CCEE: context     | @#55CCEE: $ f:X\to Y $ |
| $y\in \Sigma_Y$ |

| @#55EE55: postulate   | @#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]]
==== Parents ====
=== Subset of ===
[[Function]]
=== Context ===
[[Measurable space]]