Show that Xn d → X in D if Xˆn d → X in D and X n −Xˆ n d → 0. Do this by proving and applying the property that if X n d → X in D and Yn d → y in D for non-random y, then (X n , Y n ) d → (X, y) in...

Show that Xn d → X in D if Xˆn d → X in D and X_n−Xˆ_n
d → 0. Do this by proving and applying the property that if X_n
d → X in D and Yn d → y in D for non-random y, then (X_n, Y_n) d → (X, y) in D2 and X_n
+ Y_n
d → X + y in D, when X has continuous paths a.s.