AS the rigorous justification of Bellissard's theory [B2], we define a
nd calculate the non-diagonal component of the conductivity tensor (ca
lled the Hall conductivity) of the 2-dimensional electron system in a
uniform magnetic field. Our model is the 2-dimensional Schrodinger ope
rator with uniform magnetic and electric fields. To calculate the Hall
conductivity concretely, we consider Abel limit. (C) Elsevier, Paris.