We report detection of the edge channel of a two-dimensional electron gas (
2DEG) in quantum Hall regime, through the measurement of the chemical poten
tial variation and the compressibility of a 2DEG using a single-electron tr
ansistor (SET) on top of the 2DEG. The measurements at higher frequencies e
nabled us to detect the incompressible electronic states of the fractional
quantum Hall effect (FQHE), the results of which indicate a method for reso
lving the edge channel of FQHE spatially.