 In a later article, Aumann (1987) argues that the assumptions that \(\Omega\) is finite and that \(\mu(\omega) \gt 0\) for each \(\omega \in \Omega\) reflect the idea that agents only regard as “really” possible a finite collection of salient worlds to which they assign positive probability, so that one can drop the states with probability 0 from the description of the state space. Aumann also notes that this result implicitly assumes that the agents have common knowledge of their partitions, since a description of each possible world includes a description of the agents’ possibility sets. And of course, this result depends crucially upon (i), which is known as the common prior assumption (CPA).