Use complexity regularization to choose the parameters of the estimate in Problem 19.4. Apply the chaining and the peeling technique in the proof of Theorem 11.2 to derive a version of Theorem 11.2...

Use complexity regularization to choose the parameters of the estimate in Problem 19.4.

Apply the chaining and the peeling technique in the proof of Theorem 11.2 to derive a version of Theorem 11.2 where one uses integrals of covering numbers of balls in the function space as in Theorem 19.3. Use this result together with Problem 19.6 to give a second proof for Theorem 19.5.