  Repeated measurements on a part of a bipartite system strongly affect the
other part not measured, whose dynamics is regulated by an effective contracted
evolution operator. When the spectrum of this operator is discrete, the latter
system is driven into a pure state irrespective of the initial state, provided
the spectrum satisfies certain conditions. We here show that even in the case
of continuous spectrum an effective distillation can occur under rather general
conditions. We confirm it by applying our formalism to a simple model.
