Hall resistance and the diamagnetic moment of periodically modulated two-dimensional systems

It is argued that the Hall resistance of macroscopic samples can be directly obtained by ensemble averaged transport properties of mesoscopic systems. The resulting formula relates the Hall current to the part of the magnetic moment of Fermi electrons, which originates in macroscopic currents only. As one of the possible application the Hall resistance of the periodically modulated two-dimensional electron system in the strong magnetic field is briefly discussed.