  We prove a version of the Stokes formula for differential forms on locally
convex spaces. The main tool used for proving this formula is the surface layer
theorem proved in another paper by the author. Moreover, for differential forms
of a Sobolev-type class relative to a differentiable measure, we compute the
operator adjoint to the exterior differential in terms of standard operations
of calculus of differential forms and the logarithmic derivative. Previously,
this connection was established under essentially stronger assumptions.
