We consider the problem of nonlinear filtering within the framework of deterministic uncertain systems (i.e. control systems with disturbances). We investigate the relationship between the two main approaches to the problems: the set- membership approach and the nonlinear Happroach. We establish an interesting connection between the two basic constructs of these two approaches: the information state and the information domain. This connection helps to establish a clearer understanding for the problem and will play a fundamental role in nonlinear robust output feedback control.