A unified topological concept of stability in terms of two measures

A new concept of stability which unifies Lyapunov and orbital stabilities as well as leading to other notions between them is defined in terms of a given topology of the function space and two different measures. An attempt is made to offer sufficient conditions to obtain stability criteria for such concepts. The employment of two measures also covers several known results in usual stability theory and therefore, the present framework provides an additional unification.