Measuring similarity between ontologies can be very useful for different purposes, e.g., finding an ontology to replace another, or finding an ontology in which queries can be translated. Classical measures compute similarities or distances in an ontology space by directly comparing the content of ontologies. We introduce a new family of ontology measures computed in an alignment space: they evaluate the similarity between two ontologies with regard to the available alignments between them. We define two sets of such measures relying on the existence of a path between ontologies or on the ontology entities that are preserved by the alignments. The former accounts for known relations between ontologies, while the latter reflects the possibility to perform actions such as instance import or query translation. All these measures have been implemented in the OntoSim library, that has been used in experiments which showed that entity preserving measures are comparable to the best ontology space measures. Moreover, they showed a robust behaviour with respect to the alteration of the alignment space.