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Quasi-regular boundary and Stokes’ formula for a sub-analytic leaf. (English) Zbl 0594.32011
Deformations, Proc. Semin., Łódź-Warsaw/Pol. 1982/84, Lect. Notes Math. 1165, 235-252 (1985).
[For the entire collection see Zbl 0568.00006.]
The author relates some differential properties of sub-analytic leaves to Whitney regularity conditions and obtains the following version of Stokes’ theorem: Let M be a p-dimensional, oriented and sub-analytic leaf in X and let $$\Sigma$$ be the quasi-regular boundary of M, and $$\epsilon$$ the induced 0-form on $$\Sigma$$ by M. Let $$\alpha$$ be a differential (p- 1)-form of class $$C^ 1$$ on X, such that the set $$\bar M\cap \sup \alpha$$ is compact. Then $$\int (d\alpha)_ M=\int \epsilon \alpha_{\Sigma}$$.
Reviewer: K.Lancaster

MSC:
 32B20 Semi-analytic sets, subanalytic sets, and generalizations 26B20 Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.)