  In a previous paper the author constructed biinvariant measures (possibly
having values in a line bundle) for a loop group LK (with compact simply
connected K) acting on the formal completion of its complexification LG. One
motivation for this was to find a geometric construction for the unitary
structure for the positive energy representations of LK. In this paper we
pursue an analogous construction for the group of diffeomorphisms of the
circle.
