Consider a family \(\FC=\{Y^\alpha\}\) of histories of a closed quantum system, for a finite (possibly very large) collection of times \(t_1, t_2, \ldots t_f\). Under appropriate conditions one can use \(T(t',t)\) to assign probabilities in a consistent way to the histories in \(\FC\), using a multi-time generalization of the Born rule. To simplify the exposition we restrict attention to situations in which all histories begin with the same normalized initial pure state \(\ket{\Psi_0}\) at a time \(t_0 &lt;t_1\), and modify the definition in \eqref{eqn13} so that it reads