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


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.


Manifold Lebesgue Measure Pairwise Disjoint Full Measure Oriented Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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

Personalised recommendations