Level sets and equivalences of moran-type sets

In the paper, we consider Moran-type sets Ea   given by sequences {ak}k=1∞ and {nk}k=1∞. we prove that Ea may be decompose into the disjoint union of level sets. Moreover, we define three type of equivalence between two dimension functions associated to two Moran-type sets, respectively, and we classify Moran-type sets by these equivalent relations.