Geodesic
On a multidimensional generalization of the tomographic problem
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 2, Tome 244 (1997), pp. 295-301 Cet article a éte moissonné depuis la source Math-Net.Ru

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The main result: if dimension of a Euclidean space with measure is high enough, only the first observation from the long series of observations with random independent choice of projection gives an essential information of the measure. 
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     author = {V. N. Sudakov},
     title = {On a multidimensional generalization of the tomographic problem},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_244_a20/}
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V. N. Sudakov. On a multidimensional generalization of the tomographic problem. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 2, Tome 244 (1997), pp. 295-301. http://geodesic.mathdoc.fr/item/ZNSL_1997_244_a20/