Random perturbations of transformations of an interval (Q1821427)

The main result is as follows: Consider a map f of the interval [0,1] which is ergodic with invariant measure \(\mu_ f\), and a Markov chain \(x_ n^{\epsilon}\) with invariant measure \(\mu^{\epsilon}\) which is a small random perturbation of f. Then \(\mu^{\epsilon}\) converges weakly to \(\mu_ f\) as \(\epsilon\to 0\).