In the paper we obtain a local zero-two law for positive contractions of $L^1$-spaces, which we use in order to offer new proofs of a theorem of Orey concerning Markov chains, and of the strong asymptotic stability of certain Markov operators that have appeared in the study of the Tjon-Wu equation and in connection with the Hannsgen and Tyson model of the cell cycle.
ZAHAROPOL, RADU (2000) "A Local Zero-Two Law and Some Applications," Turkish Journal of Mathematics: Vol. 24: No. 1, Article 8. Available at: https://journals.tubitak.gov.tr/math/vol24/iss1/8