Prove the second part of Theorem 18.1, i.e., show that the expected L2 error converges to zero for every distribution of (X, Y ) with X ∈ [0, 1] a.s. and EY 2                    E  sup f∈Tlog(n)Fn 1...

Prove the second part of Theorem 18.1, i.e., show that the expected L2 error converges to zero for every distribution of (X, Y ) with X ∈ [0, 1] a.s. and EY 2 <>

                   E  sup f∈Tlog(n)Fn 1 n n i=1 |f(Xi) − Yi,L| 2 − E{|f(X) − YL| 2 } → 0 (n → ∞).