Show that Theorem 9.6.1 is also valid for martingales relative to a joint process. That is, show that if h is a convex function of a real variable and if {Z n ; n ≥ 1} is a martingale relative to a...

Show that Theorem 9.6.1 is also valid for martingales relative to a joint process. That is, show that if h is a convex function of a real variable and if {Z_n; n ≥ 1} is a martingale relative to a joint process {Z_n, X_n; n ≥ 1}, then {h(Z_n); n ≥ 1} is a submartingale relative to {h(Z_n), X_n; n ≥ 1}.