  The definition of memory in operational approaches to quantum
non-Markovianity depends on the statistical properties of different sets of
outcomes related to successive measurement processes performed over the system
of interest. Using projectors techniques we develop a perturbation theory that
enables to expressing both joint probabilities and outcome correlations in
terms of the unperturbed system density matrix propagator. This object defines
the open system dynamics in absence of measurement processes. Successive series
terms, which are scaled by the system-environment interaction strength, consist
in a convolution structure involving system propagators weighted by higher
order bath correlations. The formalism is corroborated by studying different
dynamics that admit an exact description. Using the perturbative approach,
unusual memory effects induced by the interplay between the system-environment
interaction and measurement processes are found in finite temperature
reservoirs.
