Differential forms on locally convex spaces and the Stokes formula

We prove a version of the Stokes formula for differential forms of finite codimension on a locally convex space (LCS). The main tool used to prove this formula is a surface layer theorem, previously proved by the first author. Moreover, on a subspace of differential forms of Sobolev type with respect to a differentiable measure, we obtain a formula expressing the operator adjoint to the exterior differential via standard operations of the calculus of differential forms and the logarithmic derivative. Previously, this relation was established under stronger assumptions on the LCS, the measure, or the smoothness of the differential forms.