  A deep connection between the Hall conductance in realistic situation and a
topological invariant is pointed out based on von-Neumann lattice
representation in which Landau level electrons have minimum spatial extensions.
We show that the Hall conductance has no finite size correction in quantum Hall
regime, but a coefficient of induced Chern-Simons term in QED$_3$ has a small
finite size correction, although both of them are similar topological
invariant.
