Geodesic
Extremal estimates of probability measures and their combinatorial nature
Izvestiya. Mathematics , Tome 20 (1983) no. 3, pp. 503-533.

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The problem of finding an extremal estimate of the probability of some event under restrictions on the probabilities of other events is investigated, and it is proved to be equivalent to combinatorial problems on monotone classes of $l$-graphs. New probability inequalities are obtained as specific results. Bibliography: 22 titles. 
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A. F. Sidorenko. Extremal estimates of probability measures and their combinatorial nature. Izvestiya. Mathematics , Tome 20 (1983) no. 3, pp. 503-533. http://geodesic.mathdoc.fr/item/IM2_1983_20_3_a5/

[1] Mantel W., “Vraagstuk XXVIII”, Wiskimdige Opgaven met de Oplossingen, 10:1 (1907), 60–61 | Zbl

[2] Turan P., “Egy grételméleti szélsöertékfeladatról”, Mat. és Fiz. Lapok, 48:3 (1941), 436–453 | MR

[3] Stechkin B. S., “Neskolko kombinatornykh problem”, Zbornik radova Matem. inst., Nova ser., 2 (1977), 129–137 | Zbl

[4] Katona D., Stechkin B. S., “Kombinatornye chisla, geometricheskie konstanty i veroyatnostnye neravenstva”, Dokl. AN SSSR, 251:6 (1980), 1293–1296 | MR | Zbl

[5] Sidorenko A. F., Stechkin B. S., “Ekstremalnye geometricheskie konstanty”, Matem. zametki, 29:5 (1981), 691–709 | MR

[6] Katona D., “Neravenstva dlya raspredeleniya dliny summy sluchainykh vektorov”, Teor. ver. i ee prim., XXII:3 (1977), 466–481 | MR

[7] Katona G. O. H., “Continuous versions of some extremal hypergraph problems”, Combinatorics, North-Holland publ. comp., N. Y., 1978, 653–678 | MR

[8] Sidorenko A. F., “Klassy gipergrafov i veroyatnostnye neravenstva”, Dokl. AN SSSR, 254:3 (1980), 540–543 | MR | Zbl

[9] Erdös P., Simonovits M., “A limit theorem in graph theory”, Studia Scient. Math. Hungar., 1:1–2 (1966), 51–57 | MR | Zbl

[10] Brown W. G., Erdös P., Simonovits M., “Extremal problems for directed graphs”, Journal of Comb. Theory (B), 15:1 (1973), 77–93 | DOI | MR | Zbl

[11] Sidorenko A. F., “Metod kvadratichnykh form v kombinatornoi probleme Turana”, Vestnik Mosk. un-ta, ser. matem., mekhan., 1982, no. 1, 3–6 | MR | Zbl

[12] Sidorenko A. F., “O sistemakh mnozhestv, obladayuschikh $T$-svoistvom”, Vestnik Mosk. un-ta, ser. matem., mekhan., 1981, no. 5, 19–22 | MR | Zbl

[13] Goodman A. W., “On the sets acquaintances and strangers at any party”, Amer. Math. Monthly, 66:9 (1959), 778–783 | DOI | MR | Zbl

[14] Giraud G., “Sur le probléme de Goodman pour le quadrangles et la majoration des nombres de Ramsey”, Journal of Comb. Theory (B), 27:3 (1979), 237–253 | DOI | MR | Zbl

[15] Sidorenko A. F., “O chislakh Turana $T(n, 5, 4)$ i kolichestve monokhromaticheskikh 4-klik v 2-rastsvechennom 3-grafe”, Voprosy kibernetiki, 1980, no. 64, 117–124 | Zbl

[16] Erdös P., “On the number of complete subgraphs contained in certain graphs”, Magyar tud. akad. math. kutató int. közl., 7:3 (1962), 459–464 | MR | Zbl

[17] Lorden G., “Blue-empty chromatic graphs”, Amer. Math. Monthly, 69:2 (1962), 114–120 | DOI | MR | Zbl

[18] Brown W. G., Harary P., “Extremal digraphs”, Combinatorial theory and its applications, North-Holland publ. comp., N.,Y., 1970, 135–198 | MR

[19] Baumert L. D., McEliece R. J., Rodemich E. R., Rumsey H., “A probabilistic version of Sperner's theorem”, ARS Combinatoria, 9 (1980), 91–100 | MR | Zbl

[20] Kleithman D., “A conjecture of Erdös–Katona on commensurable pairs among subsets of an $n$-set”, Theory of graphs, Acad. Kiadó, Budapest, 1968, 187–207 | MR

[21] Levenshtein V. I., “O granitsakh dlya upakovok v $n$-mernom evklidovom prostranstve”, Dokl. AN SSSR, 245:6 (1979), 1299–1303 | MR

[22] Erdös P., Moon J. W., “On the subgraphs of the complete bipartite graph”, Canad. Math. Bull., 7:1 (1964), 35–39 | MR | Zbl