  We propose a functional measure over the torsion tensor. We discuss two
completely equivalent choices for the Wheeler-DeWitt supermetric for this
field, the first one being based on its algebraic decomposition, the other
inspired by teleparallel theories of gravity. The measure is formally defined
by requiring the normalization of the Gaussian integral. To achieve such a
result we split the torsion tensor into its spin-parity eigenstates by
constructing a new, York-like, decomposition. Of course, such a decomposition
has a wider range of applicability to any kind of tensor sharing the symmetries
of the torsion. As a result of this procedure a functional Jacobian naturally
arises, whose formal expression is given exactly in the phenomenologically
interesting limit of maximally symmetric spaces. We also discuss the explicit
computation of this Jacobian in the case of a $4$-dimensional sphere $S^4$ with
particular emphasis on its logarithmic divergences.
