  We define holonomic measures to be certain analogues of varifolds that keep
track of the local parameterization and orientation of the submanifold they
represent. They are Borel measures on the direct sum of several copies of the
tangent bundle.
  We show that there is an approximation to these by smooth singular chains
whose boundaries and Lagrangian actions are controlled.
  As an illustration of the usefulness of this result, we show how this can be
applied to study foliations on the torus. We give other applications elsewhere.
