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Generalization of one Poletskii lemma to classes of space mappings

  • E. A. Sevost’yanov
Article

The paper is devoted to investigations in the field of space mappings. We prove that open discrete mappings fW 1,n loc such that their outer dilatation K O (x, f) belongs to L n−1 loc and the measure of the set B f of branching points of f is equal to zero have finite length distortion. In other words, the images of almost all curves γ in the domain D under the considered mappings f : D → ℝ n , n ≥ 2, are locally rectifiable, f possesses the (N)-property with respect to length on γ, and, furthermore, the (N)-property also holds in the inverse direction for liftings of curves. The results obtained generalize the well-known Poletskii lemma proved for quasiregular mappings.

Keywords

Space Mapping Quasiconformal Mapping Topological Index Absolute Continuity Normal Domain 
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.

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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  • E. A. Sevost’yanov
    • 1
  1. 1.Institute of Applied Mathematics and MechanicsUkrainian National Academy of SciencesDonetskUkraine

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