  Continuing the work started in Part I and II of this series (see
q-alg/9706004 and math.QA/9801049), we prove the relationship between the
Aarhus integral and the invariant $\Omega$ (henceforth called LMO) defined by
T.Q.T. Le, J. Murakami and T. Ohtsuki in q-alg/9512002. The basic reason for
the relationship is that both constructions afford an interpretation as
"integrated holonomies". In the case of the Aarhus integral, this
interpretation was the basis for everything we did in Parts I and II. The main
tool we used there was "formal Gaussian integration". For the case of the LMO
invariant, we develop an interpretation of a key ingredient, the map $j_m$, as
"formal negative-dimensional integration". The relation between the two
constructions is then an immediate corollary of the relationship between the
two integration theories.
