I'm reading a engeneering book (Turbulent Flow - Pope) and it isn't very rigorous.
Let $X(t)$ be a casual variable, for every fixed $t\in \mathbb{R}$.
How can we define the derivative with respect to $t$?
What are the assumptions that allow $\partial_t\mathbb{E}[X]=\mathbb{E}[\partial_tX]$