Show that the process \(f^{2} \bullet\langle Mangle_{t}:=\int_{0}^{t}|f(s)|^{2} d\langle Mangle_{s}\) appearing in Theorem 17.9.b) is adapted.

Data From 17.9 Theorem 

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17.9 Theorem. Let (Mt, ter be in M satisfying (DM), write for the measure induced by the increasing process (M), and let f = C(M). Then we have for all t < T a) ff. Mis a linear map from (M) into M, L.e. (f Mt)t&T is a continuous L martingale;