  The thermodynamic potential of an ideal nonrelativistic gas of
two-dimensional electrons in crossed uniform magnetic and electric fields is
constructed. For low temperatures and very weak electric fields, it is shown
that the Hall conductance is always quantized at integral multiples of $e^2/h$
over a large range of strong magnetic fields. This could be viewed as a quantum
statistical explanation of the integral quantum Hall effect. Magnetic
properties of the system at high temperatures are briefly discussed.

Condensed Matter