A sufficient statistic $T$ for the parameter $\theta$ is said to be complete if and only if: $$ E(g(T)) = 0 \ \ \forall \theta \Leftrightarrow g(T) = 0$$
Then it's said that a vector$\mathbf{T}$ with length $k$ of sufficient statistics is complete if they are in a k-dimensional rectangle.
I didn't get the last paragraph. Why is it said so? Could you give me an example to illustrate that?
Thank you! :)