  We have investigated the local magneto-transport in high-quality 2D electron
systems at low carrier densities. The positive magneto-resistance in
perpendicular magnetic field in the strongly insulating regime has been
measured to evaluate the spatial concentration of localized states within a
mesoscopic region of the samples. An independent measurement of the electron
density within the same region shows an unexpected correspondence between the
density of electrons in the metallic regime and that of the localized states in
the insulating phase. We have argued that this correspondence manifests a rigid
distribution of electrons at low densities.
