Show that the estimate in Theorem 14.6 satisfies                                   E  |mn(x) − m(x)| 2 µ(dx) ≤ c · C2/(2p+1) log2(n) n 2p/(2p+1) for every p ≤ M + 1 and every distribution of (X, Y )...

Show that the estimate in Theorem 14.6 satisfies

                                  E  |mn(x) − m(x)| 2 µ(dx) ≤ c · C2/(2p+1) log2(n) n 2p/(2p+1)

for every p ≤ M + 1 and every distribution of (X, Y ) with supp(X) ⊆ [0, 1], |Y | ≤ L a.s., and m (p, C)-smooth. Hint: Apply Problem 14.3.