Changes

::<math>\chi_{\mathbb Q}(x) =

::<math>\chi_{\mathbb Q}(x) =

\begin{cases}

\begin{cases}

   1 & \mbox{if } x \in \mathbb Q, \\

   1 & \mbox{if } x \in \mathbb{Q}, \\

   0 & \mbox{if } x \notin Q

   0 & \mbox{if } x \notin \mathbb{Q}

\end{cases}</math>.

\end{cases}</math>.

Because the rationals are only countable, this function is zero "almost everywhere": there are far more irrationals than rationals, and the function is <math>0</math> at all of these.  Thus we would expect that  

Because the rationals are only countable, this function is zero "almost everywhere": there are far more irrationals than rationals, and the function is <math>0</math> at all of these.  Thus we would expect that