Geodesic
Verification of data in certain problems of linear programming and the generalized Bernshtein problem
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 8 (2005) no. 3, pp. 231-244 
S. É. Lugovkin. Verification of data in certain problems of linear programming and the generalized Bernshtein problem. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 8 (2005) no. 3, pp. 231-244. http://geodesic.mathdoc.fr/item/SJVM_2005_8_3_a4/
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     author = {S. \'E. Lugovkin},
     title = {Verification of data in certain problems of linear programming and the generalized {Bernshtein} problem},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {231--244},
     year = {2005},
     volume = {8},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2005_8_3_a4/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We study the problem of finding the necessary and sufficient conditions of the fact that a given set of numbers could be a set of probabilities of certain events and probabilities of the pairwise interselection of such events. The algorithm of building a system of inequalities for solving this problem is obtained. The application of this algorithm to more general problems is discussed.

[1] Nechepurenko M. I., “Intervalnye otsenki v bulevykh modelyakh nadezhnosti”, Tr. IVMiMG SO RAN. Ser. Sistem. modelirovanie, 4(22), Novosibirsk, 1997, 101–112

[2] Bernshtein S. N., Teoriya veroyatnostei, GTTI, M.-L., 1934

[3] Lugovkin S. E., Ob odnoi zadache Bernshteina (sluchai chetyrekh sobytii), Preprint / RAN. Sib. otd-nie. IVMiMG; 1158, Novosibirsk, 2003