Abstract: This note reports the observation that many of the results introduced by Aumann in his first 1974 formulation of correlated equilibrium do not rely on action spaces being finite. The central assumption guarantees that even when players have different subjective probability assessments, there are enough events on which there is intersubjective agreement. Exactly the same assumptions guarantee intersubjective agreement on a much richer family of events. This makes it possible to generalize many results straightforwardly to a continuum of actions.