I know that, if $X$ is independent of $Y$, it holds
$$E[g(X,Y)|Y]=\int_\Omega g(X(\omega),Y)dP(\omega)$$
Does this apply, if $Y$ is not only one random variable, but let's say a vector of random variables? Can $X$ be a vector of random variables, too?
A book or reference for that would be great!
Thank you in advance!