Overview
In order to be able to integrate (in a measure theory sense) a function, the function must meet the measurability requirement. (see below)
Measurable Function
A function {% f:\Omega \rightarrow \mathbb{R} %} on the measurable space {% (\Omega, \mathcal{F}) %} is measurable if
{% f^{-1}(I) \in \mathcal{F} %}