Given a birational self-map of a compact complex surface, it is
useful to find an invariant measure that relates the dynamics of
the map to its action on cohomology. Under a very weak hypothesis
on the map, we show how to construct such a measure. The main
point in the construction is to make sense of the wedge product of
two positive, closed (1, 1)-currents. We are able to do this
in our case because local potentials for each current have
``finite energy'' with respect to the other. Our methods also
suffice to show that the resulting measure is mixing, does not
charge curves, and has nonzero Lyapunov exponents.