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Abstract: The economic literature with a measure space of agents is enormous, where one usually works with an atomless countably additive measure space to model individual negligibility. However, there have been a number of attempts to drop the countable additivity assumption by working with countably many agents with a purely finitely additive measure. The main purpose of this paper is to illustrate the necessity of countable additivity in modeling infinitely many agents in terms of the existence of equilibria and the idealized limit property in general equilibrium theory and game theory.