  The induced Chern-Simons term for a paired electron state is calculated in
the quantum Hall system by using a field theory on the von Neumann lattice. The
coefficient of the Chern-Simons term, which is the Hall conductance, has not
only the usual term proportional to a filling factor due to P (parity) & T
(time reversal) symmetry breaking but also correction terms due to P & T & U(1)
symmetry breaking. The correction term essentially comes from the
Nambu-Goldstone mode and depends on an infrared limit. It is shown that the
correction term is related to a topological number of a gap function in the
momentum space.
