View source for Composition of measurable maps is measurable

{{Todo|write this - as it's mostly copied from the measurable map page}}
==Statement==
Given two [[Measurable map|measurable maps]] their composition is measurable<ref name="PAS">Probability and Stochastics - Erhan Cinlar</ref>:
* {{M|f:(A,\mathcal{A})\rightarrow(B,\mathcal{B})}} is measurable (same as saying: {{M|f:A\rightarrow B}} is {{M|\mathcal{A}/\mathcal{B} }}-measurable) and
* {{M|g:(B,\mathcal{B})\rightarrow(C,\mathcal{C})}} is measurable 
then:
* {{M|g\circ f:(A,\mathcal{A})\rightarrow(C,\mathcal{C})}} is measurable.

In effect:
* {{M|\mathcal{A}/\mathcal{B} }}-measurable followed by {{M|\mathcal{B}/\mathcal{C} }} measurable {{M|1==}} {{M|\mathcal{A}/\mathcal{C} }}-measurable
==Proof==
{{Todo|See<ref name="PAS"/> page 6 if help is needed (it wont be)}}
==References==
<references/>
{{Theorem Of|Measure Theory}}