On some results on the stability of Markov operators

Abstract: We formulate a criterion for the existence of an invariant measure for a Feller semigroup defined on a metric space with the e-property for bounded continuous functions and use it to prove the asymptotic stability of a semigroup satisfying a lower bound condition. Our results complement those of A. Lasota and J. A. Yorke in proper metric spaces and of T. Szarek in Polish spaces.