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Threshold functions. (English) Zbl 0648.05048
It is shown that every non-trivial monotone increasing property of subsets of a set has a threshold function. This generalizes a number of classical results in the theory of random graphs.

MSC:
05C80 Random graphs (graph-theoretic aspects)
60C05 Combinatorial probability
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References:
[1] B. Bollobás,Random Graphs, Academic Press, London, 1985.
[2] G. Katona, A theorem of finite sets, in:Theory of Graphs (P. Erdös and G. Katona, eds), Academic Press, New York, 1968, 187–207.
[3] J. B. Kruskal, The number of simplices in a complex, in:Math. Optimization Techniques, Univ. Calif. Press, Berkeley and Los Angeles, 1963, 251–278.
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