  We re-examine the issue of local counter terms in the analysis of quantum
anomalies. We analyze two-dimensional theories and show that the notion of
local counter terms need to be carefully defined depending on the physics
contents such as whether one is analyzing gauge theory or bosonization. It is
shown that a part of the Jacobian, which is apparently spurious and eliminated
by a local counter term corresponding to the mass term of the gauge field in
gauge theory, cannot be removed by a {\it local} counter term and plays a
central role by giving the kinetic term of the bosonized field in the context
of path integral bosonization.
