In the below picture encircled in red:
If $L_D(h) = E_{z \text{~} D}[l(h, z)]$,
Then how is $L_D(h) = E_{S' \text{~} D^m}[L_{S'}(h)] $?
I see that $$\large L_D(h) = E_{z \in Z}[l(h, z)] = \sum_{z \in Z} l(h,z)D(z)$$ where $D$ is the distribution on $Z$ the set of samples. The first equation should be defined as:
$$\large E_{S' \text{~} D^m}[L_{S'}(h)] = \sum_{S'}[\frac{1}{m}\sum_{z_i \in S'}l(h,z_i)]D^m(S')$$
But how are these two qual?
