| Summary: | This paper obtains a measure-theoretic restriction that must be satisfied by a prior probability measure for posteriors to be computed in limited time. Specifically, it is shown that the prior must be factorizable. Factorizability is a set of independence conditions for events in the sample space that allows agents to calculate posteriors using only a subset of the dataset. The result has important implications for models in mathematical economics and finance that rely on a common prior. If one introduces the limited time restriction to Aumann’s famous <i>Agreeing to Disagree</i> setup, one sees that checking for factorizability requires agents to have access to every event in the measure space, thus severely limiting the scope of the agreement result.
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