  From a path integral point of view (e.g. \cite{Q98}) physicists have shown
how {\it duality} in antisymmetric quantum field theories on a closed
space-time manifold $M$ relies in a fundamental way on Fourier Transformations
of formal infinite-dimensional volume measures. We first review these facts
from a measure theoretical point of view, setting the importance of the Hodge
decomposition theorem in the underlying geometric picture, ignoring the local
symmetry which lead to degeneracies of the action. To handle these degeneracies
we then apply Schwarz's Ansatz showing how duality leads to a factorization of
the analytic torsion of $M$ in terms of the partition functions associated to
degenerate "dual" actions, which in the even dimensional case corresponds to
the identification of these partition functions.
