Geodesic
Two close sets of bounded variation
Matematičeskie zametki, Tome 19 (1976) no. 4, pp. 653-656.

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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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     author = {V. S. Meilanov},
     title = {Two close sets of bounded variation},
     journal = {Matemati\v{c}eskie zametki},
     pages = {653--656},
     publisher = {mathdoc},
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     number = {4},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_4_a19/}
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V. S. Meilanov. Two close sets of bounded variation. Matematičeskie zametki, Tome 19 (1976) no. 4, pp. 653-656. http://geodesic.mathdoc.fr/item/MZM_1976_19_4_a19/