["Bulletin of Economic Research, EarlyView. ", "\nABSTRACT\nThis paper states and proves four different properties that the steady state of any infinite‐dimensional economy, represented by an infinite sequence, satisfies and provides a mathematically rigorous sufficient condition that characterizes β‐convergence. Examples of infinite‐dimensional economies are abound in autonomous infinite‐horizon dynamic optimization models and general equilibrium models with infinitely many goods, time periods, or states of the world. The terms of the sequence that represents the economy may refer to consumption, labor supply, productive capital, state contingent securities, debt, prices, and so on. The properties introduced are uniqueness${\\it uniqueness}$, anonymity${\\it anonymity}$, invariance, and convergence${\\it convergence}$."]