Validity condition for Instrumental Variables My professor states the validity condition in the following way:
$W$ (the matrix of instrumental variables) must be such that 
$ \text{plim} \, \frac{W'u}{N}=0$, where $u$ is the error term.
Intuitively, I can see that in some way, this relates to the covariance between $W$ and $u$, but am not entirely convinced.
Moreover, why do we look at this condition in an asymptotic setting? Why not impose mean independence, i.e., $E(u|W)=E(u)$?
Essentially, $Cov(u,W) = 0$ is implied by $E(u|W) = E(u)$ by the Law of iterated expectations