Definition (Accessible)

Let $X_{n},n\ge0$ be a MC, with transition matrix $P$ and the state space $S$. Let $i,j\in S$ be two states. We say $i$ leads to $j$ if the probability of reaching $j$ from $i$ is positive i.e. $$P_{i}(X_{n}=j \mbox{ for some }n\ge0)=1$$and write $i\to j$. If $i\to j$ we also say $j$ is accessible from $i$.