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We create laterally large and low-disorder GaAs quantum-well-based quantum dots that act as small two-dimensional electron systems. We monitor tunneling of single electrons to the dots by means of capacitance measurements and identify single-electron capacitance peaks in the addition spectrum from occupancies of one up to thousands of electrons. The data show two remarkable phenomena in the Landau level filling factor range ν=2 to ν=5 in selective probing of the edge states of the dot (i) Coulomb blockade peaks arise from the entrance of
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