  We construct one Yang-Mills measure on a compact surface for each isomorphism
class of principal bundles over this surface. For this, we define a new
discrete gauge theory which is essentially a covering of the usual one. We
prove that the measures correponding to different isomorphism classes of
bundles or to different total areas of the surface are mutually singular. We
give also a combinatorial computation of the partition functions based on the
formalism of fat graphs.
