Why a positive recurrent Markov chain implies positive limiting probability?

Question

Let $X=\{X_0,X_1,\ldots\}$ be an irreducible, positive recurrent, and aperiodic Markov chain with the state space $S=\{0,1,2,\ldots\}$ then how do we show that the probability $$ \lim_{n\rightarrow\infty}P(X_n=k\mid X_0=j) $$ is independent of $j$ and strictly positive? That is, why $$ \lim_{n\rightarrow\infty}P(X_n=k\mid X_0=j)=g(k)>0? $$