The magnetic field dependence of the chemical potential of a two-dimen
sional electron system (2DES), realized in a GaAs/Al0.33Ga0.67As heter
ostructure, is measured by using a metallic single-electron transistor
(SET) on top of the 2DES. At low magnetic fields, the Landau level de
population with increasing magnetic field is observed. At high magneti
c fields, charge fluctuations are detected within the quantum-Hall reg
ime. The insulator-like behavior of the 2DES in the quantum-Hall regim
e is demonstrated by controlling the SET by a metal-gate electrode und
erneath the 2DES. (C) 1998 Elsevier Science B.V. All rights reserved.