 In summary, the histories approach resolves both quantum measurement problems M1 and M2 by introducing appropriate stochastic families of histories. In order to describe the measurement outcome as a pointer position one needs an appropriate projective decomposition of the identity—\(\{[m^j]\}\) in the simplest model or the more general \(\{M^k\}\) of   section 7.4—associated with the pointer positions. Similarly, in order to discuss how properties of the microscopic particle before the measurement are related to measurement outcomes, one needs a decomposition at \(t_1\) that includes these properties, the \([s^j]\) in \eqref{eqn23} for the simple model or the \(\xi^{jk}\) in \eqref{eqn38} for a generalized measurement. There is no fundamental quantum principle that forces one to use these decompositions. The choice is based on utility, and illustrates the importance of principle R4 in   section 5. If one wants to discuss measurements as measurements, one needs to adopt a framework in which the associated concepts make sense. And, since it is often misunderstood, it is worth emphasizing that neither the validity nor the utility of a particular framework is in any way reduced by the existence of other frameworks which are incompatible (or incommensurate) with it.