From Ritter's Book (Stochastic). Please help me give a detailed proof of this theorem.

Given: a filtration F = (Ft)ter with I = [0,20[ on (2, A, P), which satisfies the usual condi- tions, as well as real-valued processes X = (X4)ter and M = (M)ter E MS. Definition. For Y E M; let || Y ||* = (Y?), tel as well as 00 |Y|| = 2-.(14 ||Y||:) t=1 Note: for Y e M; the map t HE(Y??) is monotonically increasing. In the following we identify indistinguishable elements of Ms. Theorem. M is a complete metric space w.r.t. the metric defined by (Y,Z) ||Y - 2||. Given: a filtration F = (Ft)ter with I = [0,20[ on (2, A, P), which satisfies the usual condi- tions, as well as real-valued processes X = (X4)ter and M = (M)ter E MS. Definition. For Y E M; let || Y ||* = (Y?), tel as well as 00 |Y|| = 2-.(14 ||Y||:) t=1 Note: for Y e M; the map t HE(Y??) is monotonically increasing. In the following we identify indistinguishable elements of Ms. Theorem. M is a complete metric space w.r.t. the metric defined by (Y,Z) ||Y - 2||