Abstract
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.
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V. S. Meilanov, “Sequences of sets of bounded variation which converge in the deviation metric,” Matem. Zametki,15, No. 4, 521–526 (1974).
A. G. Vitushkin, Multidimensional Variations of Sets [in Russian], Gostekhizdat, Moscow (1955).
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Translated from Matematicheskie Zametki, Vol. 19, No. 4, pp. 653–656, April, 1976.
The author acknowledges the comments of L. D. Ivanov.
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Meilanov, V.S. Two close sets of bounded variation. Mathematical Notes of the Academy of Sciences of the USSR 19, 393–394 (1976). https://doi.org/10.1007/BF01156805
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DOI: https://doi.org/10.1007/BF01156805