I'm looking for a counter example as simple as possible.
I've learned that if X is a stochastic variable, it holds that
\begin{align}E[X | X] = X E[1 | X]\qquad (1) \end{align}
since X is measurable with regards to it's own sigma-algebra.
Moreover I have that
\begin{align}E[f(X) | X] = f(X) E[1 | X] \qquad (2) \end{align}
if $f$ is measurable function.
I'm looking for some kind of setup where (2) isn't true.