Geodesic
An integral estimate for deviations of sets in sections
Izvestiya. Mathematics , Tome 13 (1979) no. 2, pp. 261-276

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Under certain natural assumptions it is proved that for two compact sets close in the Hausdorff metric the average distance between plane sections of them is also small. Bibliography: 4 titles. 
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     author = {G. Yu. Zaitsev},
     title = {An integral estimate for deviations of sets in sections},
     journal = {Izvestiya. Mathematics },
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     volume = {13},
     number = {2},
     year = {1979},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1979_13_2_a3/}
}
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G. Yu. Zaitsev. An integral estimate for deviations of sets in sections. Izvestiya. Mathematics , Tome 13 (1979) no. 2, pp. 261-276. http://geodesic.mathdoc.fr/item/IM2_1979_13_2_a3/