Geodesic
Probabilities of complex events and the linear programming
Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 2, pp. 344-347 
S. A. Pirogov. Probabilities of complex events and the linear programming. Teoriâ veroâtnostej i ee primeneniâ, Tome 13 (1968) no. 2, pp. 344-347. http://geodesic.mathdoc.fr/item/TVP_1968_13_2_a13/
@article{TVP_1968_13_2_a13,
     author = {S. A. Pirogov},
     title = {Probabilities of complex events and the linear programming},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {344--347},
     year = {1968},
     volume = {13},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1968_13_2_a13/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The following two extremal problems are solved in the paper by methods of the linear programming. A. Let $\varepsilon\le1$ be a fixed positive number. Call the distance $\rho(A,B)$ between two events $A$ and $В$ the measure of their symmetrical difference. How many events with mutual distances not less than $\varepsilon$ can be constructed? B. Let $k be fixed integers and $0. For what $c$ is it possible to choose $k$ events with the probability of their intersection not less than $c$ from every $n$ events with the probabilities not less than $p$? The second problem was investigated in [1] by a different method. We reduce both the problems to finding of extrema of some linear forms on rather simple convex polyhedrons.