  The sets of after-measurement states for standard and generalized quantum
measurements are compared. It is shown that for a SIC-POVM generalized
measurement, the ratio of the volume of the set of after-measurement states and
the volume of the simplex generated by individual outcomes quickly tends to
zero with increase of the number of dimensions. The volumes used are based on
the Hilbert-Schmidt norm. Some consequences on actual realizations, having
finite collections of systems are discussed.
