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

Wikipedia: Sigma-algebra

Parents

Subset of

Function

Context

Measurable space