Geodesic
Exceptional directions for a~convex body
Matematičeskie zametki, Tome 20 (1976) no. 3, pp. 365-371.

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Let $K$ be a convex body in Rn andO be a point inside $K$. We examine the Grassmann manifold of $k$-planes passing through $O$. We take as exceptional the planes intersecting $K$ along a body having at least one $(k-1)$-dimensional face such that it does not have points inside the hyperfaces of body $K$. We prove that in the Grassmann manifold $G_k^n$ the set of such exceptional planes is of measure zero. 
@article{MZM_1976_20_3_a7,
     author = {B. A. Ivanov},
     title = {Exceptional directions for a~convex body},
     journal = {Matemati\v{c}eskie zametki},
     pages = {365--371},
     publisher = {mathdoc},
     volume = {20},
     number = {3},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_3_a7/}
}
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B. A. Ivanov. Exceptional directions for a~convex body. Matematičeskie zametki, Tome 20 (1976) no. 3, pp. 365-371. http://geodesic.mathdoc.fr/item/MZM_1976_20_3_a7/