 Note that Aumann’s definition of \(\omega\)-Bayesian rationality implies that \(\mu_i (\mathcal{H}_i (\omega)) \gt 0\), so that the conditional expectations are defined. Aumann’s main result, given next, implicitly assumes that \(\mu_i (\mathcal{H}_i (\omega)) \gt 0\) for every agent \(i \in N\) and every possible world \(\omega \in \Omega\). This poses no technical difficulties if the CPA is satisfied, or even if the priors are only mutually absolutely continuous, since if this is the case then one can simply drop any \(\omega\) with zero prior from consideration.