  We study sequential measurement scenarios where the system is repeatedly
subjected to the same measurement process. We first provide examples of such
repeated measurements where further repetitions of the measurement do not
increase our knowledge on the system after some finite number of measurement
steps. We also prove, however, that repeating the L\"uders measurement of an
unsharp two-outcome observable never saturates in this sense, and we
characterize the observable measured in the limit of infinitely many
repetitions. Our result implies that a repeated measurement can be used to
correct the inherent noise of an unsharp observable.
