Conditional expectation and consistent estimation

[mmgg]

Could someone explain the following statement:

[E(y|x,z),E(y|x),E(z|x)] are consistently estimable on the support of (x,z) if either:
1. (x,z) are discrete or,
2. [E(y|x,z),E(y|x),E(z|x)] are continuous on the support of (x,z)


Thanks!!

[Dason]

Please don't post the same thread more than once.

[mmgg]

Maybe I should add that this statement refers to a linear in mean model: y=a+bE[y|x]+E[z!x]'c+z'd+u where E[u!x,z]=x'g where a,b,c,d,g are vectors of parameters. In the paper where this model is discussed it is said that in order to proceed with the analysis one of the two assumption I reported in the previous post have to be made. Don't have any idea of why.
Thanks...