Geodesic
An estimate of the measure of the set of planes almost tangent to a~compactum with bounded variations
Izvestiya. Mathematics , Tome 16 (1981) no. 1, pp. 135-150.

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It is proved that in a Euclidean space almost all planes intersecting a compactum with finite variations are in general position with respect to it. An example is given showing that the requirement of the boundedness of the corresponding variation is necessary. Bibliography: 3 titles. 
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G. Yu. Zaitsev. An estimate of the measure of the set of planes almost tangent to a~compactum with bounded variations. Izvestiya. Mathematics , Tome 16 (1981) no. 1, pp. 135-150. http://geodesic.mathdoc.fr/item/IM2_1981_16_1_a6/

[1] Zaitsev G. Yu., “Integralnaya otsenka uklonenii mnozhestv v secheniyakh”, Izv. AN SSSR. Ser. matem., 42 (1978), 972–988 | MR

[2] Ivanov L. D., Variatsii mnozhestv i funktsii, Nauka, M., 1975 | MR

[3] Federer H., Geometric measure theory, Springer, Berlin, 1969 | MR