The fiberwise Stokes theorem says that given a differential form on a smooth fiber bundle whose fibers have boundary, the difference between the fiberwise integral of the differential and the differential of its fiberwise integral is, up to a sign, the fiberwise integral of the restriction of the form to the boundary.

Is there a citeable reference for a proof of this result? For the sake of being definite, let's say that “citeable” means indexed by Mathematical Reviews or Zentralblatt, or available on arXiv.

Of course, for such a well-known result I would very much prefer an older, classical reference as opposed to something recent on arXiv.

Citeable reference for a statement of this theorem without proof do exist, the earliest one that I am aware of is Greub-Halperin-van Stone I, Chapter VII, Problem 4.

The fiberwise Stokes theorem says that given a differential form on a smooth fiber bundle whose fibers have boundary, the difference between the fiberwise integral of the differential and the differential of its fiberwise integral is, up to a sign, the fiberwise integral of the restriction of the form to the boundary.

Is there a citeable reference for a proof of this result? For the sake of being definite, let's say that “citeable” means indexed by Mathematical Reviews or Zentralblatt, or available on arXiv.

Of course, for such a well-known result I would very much prefer an older, classical reference as opposed to something recent on arXiv.

Citeable reference for a statement of this theorem without proof do exist, the earliest one that I am aware of is Greub-Halperin-van Stone I, Chapter VII, Problem 4. References which do not include proofs will not suffice for my purposes.

The fiberwise Stokes theorem says that given a differential form on a smooth fiber bundle whose fibers have boundary, the difference between the fiberwise integral of the differential and the differential of its fiberwise integral is, up to a sign, the fiberwise integral of the restriction of the form to the boundary.

Is there a citeable reference for this result? For the sake of being definite, let's say that “citeable” means indexed by Mathematical Reviews or Zentralblatt, or available on arXiv.

Of course, for such a well-known result I would very much prefer an older, classical reference as opposed to something recent on arXiv.

Citeable reference for a statement of this theorem without proof do exist, the earliest one that I am aware of is Greub-Halperin-van Stone I, Chapter VII, Problem 4.

The fiberwise Stokes theorem says that given a differential form on a smooth fiber bundle whose fibers have boundary, the difference between the fiberwise integral of the differential and the differential of its fiberwise integral is, up to a sign, the fiberwise integral of the restriction of the form to the boundary.

Is there a citeable reference for a proof of this result? For the sake of being definite, let's say that “citeable” means indexed by Mathematical Reviews or Zentralblatt, or available on arXiv.

Of course, for such a well-known result I would very much prefer an older, classical reference as opposed to something recent on arXiv.

Citeable reference for a statement of this theorem without proof do exist, the earliest one that I am aware of is Greub-Halperin-van Stone I, Chapter VII, Problem 4.