More precisely, a fundamental result about Markov chains is that a finite state irreducible aperiodic chain has a unique stationary distribution π  and, regardless of the initial state, the time-t distribution of the chain converges to π  as t tends to infinity.
The fundamental result about Markov chains states that a finite state irreducible aperiodic chain has a unique stationary distribution, π, and this distribution is reached by the time-t distribution of the chain as t approaches infinity, regardless of the initial state.