  Concentrating on finite dimensional systems, we show that one can limit to
extremal rank-1 POVMs if two simple procedures of mixing and relabeling are
permitted. We demonstrate that any finite outcome POVM can be obtained from
extremal rank-1 POVMs with these two procedures. In particular, extremal POVMs
with higher rank are just relabelings of extremal rank-1 POVMs and their
structure is therefore clarified.
