 We shall take (2) as defining ‘candidate probabilities’. In general these probabilities exhibit interference, in the sense that summing over them is not equivalent to omitting the intermediate projections in (2) (‘coarse-graining’ the histories). In the special cases in which the interference terms vanish for any pair of distinct histories, we say that the set of histories satisfies the consistency or (weak) decoherence condition. It is easy to see that this condition takes the form