Suppose that X0,X1, . . . is a sequence of random variables defined on the probability space (Ω,A, P). If g : (R, B1) → (R, B1) is a continuous function, then show that

(1) If Xn

−a−.s→. X0 then g(Xn) −a−.s→. g(X0).

(2) If Xn p−

→ X0 then g(Xn) p−

→ g(X0).

(3) If Xn d−

→ X0 then g(Xn) d−

→ g(X0).