Proposition 2.9 (Stokes’ formula) [034Z] Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
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Proposition 2.9 (Stokes’ formula)
Let σ \sigma n n ℝ {\mathbb{R}} U U N ℝ N_{\mathbb{R}} η ′ ∈ A c n − 1 , n ( U ) \eta^{\prime}\in A_{c}^{n-1,n}(U) η ′′ ∈ A c n , n − 1 ( U ) \eta^{\prime\prime}\in A_{c}^{n,n-1}(U)
∫ σ d ′ η ′ = ∫ ∂ σ η ′ , ∫ σ d ′′ η ′′ = ∫ ∂ σ η ′ . \int_{\sigma}d^{\prime}\eta^{\prime}=\int_{\partial\sigma}\eta^{\prime},\quad\int_{\sigma}d^{\prime\prime}\eta^{\prime\prime}=\int_{\partial\sigma}\eta^{\prime}.