I show that if one is only interested in local results ~ that is, theorems about what is true at a state ~ which only depend on finitely many orders of beliefs about beliefs, then the common prior assumption is essentially irrelevant. More precisely, given any model where priors have the same support and any finite N, there is another model with common priors which has the same n th order beliefs for all n  N. In this sense, priors with the same support are (locally) approximately common.