  Fix a compact 4-dimensional manifold with self-dual 2nd Betti number one and
with a given symplectic form. This article proves the following: The Frechet
space of tamed almost complex structures as defined by the given symplectic
form has an open and dense subset whose complex structures are compatible with
respect to a symplectic form that is cohomologous to the given one. The theorem
is proved by constructing the new symplectic form by integrating over a space
of currents that are defined by pseudo-holomorphic curves.
