  We show how the topological susceptibility in the Minkowskian theory of QCD
is related to the corresponding quantity in the Euclidean theory, which is
measured on the lattice. We discuss both the zero-temperature case (T = 0) and
the finite-temperature case (T > 0). It is shown that the two quantities are
equal when T = 0, while the relation between them is much less trivial when T >
0. The possible existence of ``Kogut-Susskind poles'' in the matrix elements of
the topological charge density between states with equal four-momenta turns out
to invalidate the equality of these two quantities in a strict sense. However,
an equality relation is recovered after one re-defines the Minkowskian
topological susceptibility by using a proper infrared regularization.
