Let (Xn)n=0 be a Markov chain, with state space S, and f : S N R be a function satisfying the condition:

p^n(x,y)|f(y,n)| < ,x S,n 0,

p(x, y)f (y, n + 1) = f (x, n), x S, n 0.

Prove that Mn=f(Xn,n) is a martingale with respect to (Xn).