  The classical sequential growth model for causal sets provides a template for
the dynamics in the deep quantum regime. This growth dynamics is intrinsically
temporal and causal, with each new element being added to the existing causal
set without disturbing its past. In the quantum version, the probability
measure on the event algebra is replaced by a quantum measure, which is Hilbert
space valued. Because of the temporality of the growth process, in this
approach, covariant observables (or beables) are measurable only if the quantum
measure extends to the associated sigma algebra of events. This is not always
guaranteed. In this work we find a criterion for extension (and thence
covariance) in complex sequential growth models for causal sets. We find a
large family of models in which the measure extends, so that all covariant
observables are measurable.
