An asymptotic extension of Moran construction in metric measure spaces

. In this paper, we define asymptotically generalized Cantor sets in metric measure spaces by generalizing the notion of l -similarity maps. We define the notion of ð l ; c ; n Þ -similarity maps, and extend the Moran theorem about the generalized Cantor set in R d to this general setting. As an example, we construct generalized Cantor sets in Riemannian manifolds by using ð l ; c ; n Þ -similarity maps.