=+a, and B, as defined by (5.41). Show that B1 - o2 = O(1/n), so that n- 1N > 1;

with probability 1. Show for a function f on the state space that n-1Ex- , f( X)

> LT; f(i) with probability 1. Show that n 1Ci_ 1 g(Xx, Xx+1) >

Lijm; P ;; g(i, j) for functions g on Sx S.