  In this article, we initiate a geometric measure theoretic approach to
symplectic Hodge theory. In particular, we apply one of the central results in
geometric measure theory, the Federer-Fleming deformation theorem, together
with the cohomology theory of normal cur- rents on a differential manifold, to
establish a fundamental property on symplectic Harmonic forms. We show that on
a closed symplectic manifold, every real primitive cohomology class of positive
degrees admits a symplectic Harmonic representative not supported on the entire
mani- fold. As an application, we use it to investigate the support of
symplectic Harmonic representatives of Thom classes, and give a complete
solution to an open question asked by Guillemin.
