Résumé en anglais

While the convergence properties of many sampling selection methods can be proven, there is one particular sampling selection method introduced in Baker (1987), closely related to `systematic sampling' in statistics, that has been exclusively treated on an empirical basis. The main motivation of the paper is to start to study formally its convergence properties, since in practice it is by far the fastest selection method available. We will show that convergence results for the systematic sampling selection method are related to properties of peculiar Markov chains.