 If this is satisfied, we can view (2) as defining the distribution functions for a stochastic process with the histories as trajectories. Decoherence in the sense of this abstract formalism is thus defined simply by the condition that the quantum probabilities for later events can be calculated as if the state had collapsed at the intermediate times. Qualitatively one recovers classical behaviour, in the sense that the histories are assigned quantum probabilities that nevertheless satisfy the classical formula of total probability. 