The divergence theorem and Perron integration with exceptional sets

DOI10.21136/cmj.1993.128388zbMath0789.26005OpenAlexW2725828137MaRDI QIDQ4277383

W. B. Jurkat

Publication date: 12 June 1994

Full work available at URL: https://eudml.org/doc/31335

zbMATH Keywords

generalized Riemann integraldivergence theoremsdivergence of vector fieldsnon-absolutely convergent multiple integrals

Mathematics Subject Classification ID

Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.) (26B20)

Related Items (5)

Non-absolutely convergent integrals with respect to distributions ⋮ On a generalization of Henstock-Kurzweil integrals ⋮ Integrable boundaries and fractals for Hölder classes; the Gauss-Green theorem ⋮ Non-absolutely convergent generalized Laplacian ⋮ The fundamental theorem for the $\nu_1$-integral on more general sets and a corresponding divergence theorem with singularities

Cites Work

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• The General Form of Green's Theorem
• On Mawhin's approach to multiple nonabsolutely convergent integral
• A non-absolutely convergent integral which admits $C^1$-transformations
• The surface integral
• A Characterization of Multi-Dimensional Perron Integrals and the Fundamental Theorem
• The Divergence Theorem
• A new and more powerful concept of the PU-integral
• GENERALIZED ABSOLUTELY CONTINUOUS INTERVAL FUNCTIONS AND MULTI-DIMENSIONAL PERRON INTEGRATION
• A non absolutely convergent integral which admits transformation and can be used for integration on manifolds
• On Green's Theorem

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