Phi-irreducibility
= Phi-irreducibility
{title2=$\varphi(A)>0\Longrightarrow\sum_{n\geq1}P^n(x,A)>0$}
= Phi-irreducible
{synonym}
A <Markov chain> with transition kernel $P$ is $\varphi$-irreducible if $\varphi$ is a nonzero <sigma-finite measure> and every measurable set $A$ with $\varphi(A)>0$ satisfies $\sum_{n\geq1}P^n(x,A)>0$ from every starting state $x$. This is positive reachability, not certain eventual hitting.