Abstract
In this paper we prove a variant of the Stokes formula for differential forms of a finite codimension in a locally convex space (LCS). The main tool used by us for proving the mentioned formula is the surface layer theorem for surfaces of codimension 1 in a locally convex space which was proved earlier by the first author. Moreover, on some subspace of differential forms of the Sobolev type with respect to a differentiable measure we establish a formula expressing the operator adjoint to the exterior differential via standard operations of the calculus of differential forms and the logarithmic derivative. This connection was established earlier under stronger constraints imposed either on the LCS or on the measure, or on differential forms (the smoothness condition).
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