Dimension schemas are abstract models of the data hierarchies that populate OLAP warehouses. Although there is abundant work on schma equivalence in a variety of data models. These works fo not cover dimension schemas. In this paper we propose a nation of equivalence that allows to compare dimension scheme with respect to their information capacity. The proposed notion is intended to capture dimension schema isomorphisms , and present algorihtms for testing it in well known classes of OLAP dimension schemaas . Our results also permit to compare the expressiveness of different know classes of dimention scemas