Before revision:  It is rigorously proven that continuity of either the revision protocol or the type distribution guarantees the existence of a unique solution trajectory . In many major evolutionary dynamics, an agent's switching rate between actions increases with the payoff gain from this switch, which causes nonaggregability: the current strategy composition must be identified to predict the transition of the aggregate strategy. Looking at the strategy composition, we retain equilibrium stationarity in general and  stability in potential games under admissible dynamics.
After revision:  It is rigorously proven that continuity of either the revision protocol or the type distribution guarantees the existence of a solution trajectory and for the existence of equilibrium. We confirm that equilibrium stationarity in general and stability in potential games under admissible dynamics.