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

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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. 
@article{SJVM_2005_8_3_a4,
     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},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2005_8_3_a4/}
}
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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/