Suppose P = ? Pij ? is the transition probability matrix of an irreducible recurrent Markov chain {Xn}. Use the supermartingale convergence theorem (see Remark 5.1) to show that every nonnegative solution y={y(i)} to the system of inequalities , (MISSING SUMMATION INEQUALITY) for all i is constant.
Hint: Paraphrase Example (a) of Section 6. Look at the picture attached for the entire question.