  We derive the theory of open quantum system dynamics intervened by a series
of nonselective measurements. We analyze the cases of time independent and time
dependent Hamiltonian dynamics in between the measurements and find the
approximate master equation in the stroboscopic limit. We also consider a
situation, in which the measurement basis changes in time, and illustrate it by
nonselective measurements in the basis of diabatic states of the Landau-Zener
model.
