Abstract
It is shown that every non-trivial monotone increasing property of subsets of a set has a threshold function. This generalises a number of classical results in the theory of random graphs.
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References
B. Bollobás,Random Graphs, Academic Press, London, 1985.
G. Katona, A theorem of finite sets, in:Theory of Graphs (P. Erdös and G. Katona, eds), Academic Press, New York, 1968, 187–207.
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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First author supported by NSF grant MCS 8104854