  It is well known that the quantum Hall conductivity in the presence of
constant magnetic field is expressed through the topological TKNN invariant.
The same invariant is responsible for the intrinsic anomalous quantum Hall
effect (AQHE), which, in addition, may be represented as one in momentum space
composed of the two point Green's functions. We propose the generalization of
this expression to the QHE in the presence of non-uniform magnetic field. The
proposed expression is the topological invariant in phase space composed of the
Weyl symbols of the two-point Green's function. It is applicable to a wide
range of non-uniform tight-binding models, including the interacting ones.
