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Journal of Mathematical Sciences

, Volume 141, Issue 5, pp 1545–1556 | Cite as

Integration of differential forms on manifolds with locally-finite variations. II

  • A. V. Potepun
Article
  • 19 Downloads

Abstract

In part I of the paper, we have defined n-dimensional C0-manifolds in ℝn(m ≥ n) with locally-finite n-dimensional variations (a generalization of locally-rectifiable curves to dimensionn > 1) and integration of measurable differential n-forms over such manifolds. The main result of part II states that an n-dimensional manifold that is C1-embedded into ℝm has locally-finite variations and the integral of a measurable differential n-form defined in part I can be calculated by the well-known formula. Bibliography: 5 titles.

Keywords

Manifold Lebesgue Measure Pairwise Disjoint Full Measure Oriented Manifold 
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References

  1. 1.
    G. Grauert, I. Lieb, and W. Fischer, Differential and Integralrechnung [Russian translation], Moscow (1971).Google Scholar
  2. 2.
    B. Z. Vulikh, A Brief Course of Theory of Functions of a Real Variable [in Russian], Moscow (1973).Google Scholar
  3. 3.
    B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko, Modern Geometry [in Russian], Moscow (1979).Google Scholar
  4. 4.
    N. Dinculeanu, Vector Measures, Berlin (1966).Google Scholar
  5. 5.
    A. V. Potepun, “Integration of differential forms on manifolds with locally-finite variations. I,” Zap. Nauchn. Semin. POMI, 327, 168–206 (2005).MATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • A. V. Potepun
    • 1
  1. 1.St.Petersburg State UniversitySt.PetersburgRussia

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