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1994 | 59 | 1 | 85-98
Tytuł artykułu

A descriptive, additive modification of Mawhin's integral and the Divergence Theorem with singularities

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EN
Abstrakty
EN
Modifying Mawhin's definition of the GP-integral we define a well-behaved integral over n-dimensional compact intervals. While its starting definition is of Riemann type, we also establish an equivalent descriptive definition involving characteristic null conditions. This characterization is then used to obtain a quite general form of the divergence theorem.
Twórcy
  • Abt. Mathematik II, Universität Ulm, D-89069 Ulm, Germany
Bibliografia
  • [JKS] J. Jarník, J. Kurzweil and S. Schwabik, On Mawhin's approach to multiple nonabsolutely convergent integral, Časopis Pěst. Mat. 108 (1983), 356-380.
  • [Ju-Kn] W. B. Jurkat and R. W. Knizia, A characterization of multi-dimensional Perron integrals and the fundamental theorem, Canad. J. Math. 43 (1991), 526-539.
  • [Ju-No] W. B. Jurkat and D. J. F. Nonnenmacher, A generalized n-dimensional Riemann integral and the Divergence Theorem with singularities, Acta Sci. Math. (Szeged), to appear.
  • [Ku-Jar1] J. Kurzweil and J. Jarník, Equivalent definitions of regular generalized Perron integral, Czechoslovak Math. J. 42 (117) (1992), 365-378.
  • [Ku-Jar2] J. Kurzweil and J. Jarník, Differentiability and integrability in n dimensions with respect to α-regular intervals, Results Math. 21 (1992), 138-151.
  • [Ku-Jar3] J. Kurzweil and J. Jarník, Equiintegrability and controlled convergence of Perron-type integrable functions, Real Anal. Exchange 17 (1991-92), 110-139.
  • [Maw] J. Mawhin, Generalized multiple Perron integrals and the Green-Goursat theorem for differentiable vector fields, Czechoslovak Math. J. 31 (106) (1981), 614-632.
  • [No] D. J. F. Nonnenmacher, Every M₁-integrable function is Pfeffer integrable, Czechoslovak Math. J. 43 (118) (1993), 327-330.
  • [Pf] W. F. Pfeffer, The divergence theorem, Trans. Amer. Math. Soc. 295 (1986), 665-685.
  • [Saks] S. Saks, Theory of the Integral, Dover, New York, 1964.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-apmv59z1p85bwm
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