Appendix T able of Contents

We recall Proposition 4 Proposition 4. This is due to the triangle inequality for d . There are two cases to consider. We recall Proposition 7: Proposition 7. We'll work forwards from (9), which says that E ( f) = Eψ ( f Liang et al. (2015)) with A =, B = ν, and T = F, we get EΨ null 2 sup We recall Theorem 12: Theorem 12. We'll work forwards from (10), which says that EΨ(E ( f)) EΨ null sup It follows that we can apply our "contraction lemma" for offset processes, Lemma G2, with the For (16), we first require the following lemma. Rademacher random variables and Ψ is any increasing, convex function. The proof will proceed in three lemmas which will be stated below and proved subsequently.