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Fama (1970) defined an efficient market as one in which prices always 'fully reflect' available information. This paper formalizes this definition and provides various characterizations relating to equilibrium models, profitable trading strategies, and equivalent martingale measures. These various characterizations facilitate new insights and theorems relating to efficient markets. In particular, in contrast to common belief, we show that one can test for an efficient market without the need todoi:10.2139/ssrn.1781091 fatcat:xjqfvjrmtber5dr7vubc5xhc2u