I am confused by the following expectation which appears within equation (1) of the following paper http://statweb.stanford.edu/~jhf/ftp/trebst.pdf:
$E_{X}[E_{Y}[L(Y,F(X))]|X]$
I am confused by the inner expectation, which is a expectation of $L(Y,F(X))$ with respect to Y. The result would also be $E_{X}[·|X]$ which doesn't make sense to me, since it would be the expectation with respect to the distribution of X, while conditioning on X.