In this work, the electronic properties of GaAs-based heterostructures are investigated, which contain a two-dimensional electron gas (2DEG) and a layer of self assembled InAs quantum dots in a distance of 15-40 nm. By applying a gate voltage the number of electrons per quantum dot can be precisely controlled in the range from 0-6. The respective charging events can be observed as discrete maxima in capacitance measurements. In the first part of this work it is shown, that by investigating the magnetic field dependence of the position of these maxima the oscillating Fermi energy of the two-dimensional back contact can be determined. The extracted data is in good agreement with a Gaussian Landau-level broadening. In the second part of this work, the influence of the in situ controllable number of electrons per quantum dot on the electron density and the mobility of the 2DEG is discussed. While the respective charge balances can be explained by a simple quantum capacitance model, the mobility does not follow the usually applied models for Coulomb scattering in two dimensions. The smaller the distance between the 2DEG and the quantum dots becomes, the more a resonant character of the scattering process dominates the mobility. Finally, the discussion of the electronic properties of these systems is extended to the quantum Hall effect and to novel structures, in which the 2DEG is laterally confined to a small channel. It is shown, that the interaction between the 2DEG and the quantum dots can be enhanced by such an additional lateral confinement.