Geodesic
Translation invariant measures and convex bodies
Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part X, Tome 158 (1987), pp. 146-157

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An expression is found for a translation-invariant measure on the set of planes intersecting a convex body. 
@article{ZNSL_1987_158_a14,
     author = {G. Yu. Panina},
     title = {Translation invariant measures and convex bodies},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {146--157},
     publisher = {mathdoc},
     volume = {158},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_158_a14/}
}
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G. Yu. Panina. Translation invariant measures and convex bodies. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part X, Tome 158 (1987), pp. 146-157. http://geodesic.mathdoc.fr/item/ZNSL_1987_158_a14/