Two close sets of bounded variation

  • V. S. Meilanov


If two subsets of bounded variation in Euclidean space are close in the deviation metric, then on almost all k-dimensional planes, except perhaps on a set of planes of small measure, their intersections with k-dimensional planes are also close.


Euclidean Space Bounded Variation Small Measure 
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Literature cited

  1. 1.
    V. S. Meilanov, “Sequences of sets of bounded variation which converge in the deviation metric,” Matem. Zametki,15, No. 4, 521–526 (1974).Google Scholar
  2. 2.
    A. G. Vitushkin, Multidimensional Variations of Sets [in Russian], Gostekhizdat, Moscow (1955).Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • V. S. Meilanov
    • 1
  1. 1.Dagestan Polytechnic InstituteUSSR

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