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.
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References
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A. V. Potepun, “Integration of differential forms on manifolds with locally-finite variations. I,” Zap. Nauchn. Semin. POMI, 327, 168–206 (2005).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 333, 2006, pp. 66–85.
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Potepun, A.V. Integration of differential forms on manifolds with locally-finite variations. II. J Math Sci 141, 1545–1556 (2007). https://doi.org/10.1007/s10958-007-0062-0
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DOI: https://doi.org/10.1007/s10958-007-0062-0