Threshold functions


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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First author supported by NSF grant MCS 8104854

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Bollobás, B., Thomason, A.G. Threshold functions. Combinatorica 7, 35–38 (1987).

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AMS subject classification (1980)

  • 60 C 05
  • 05 C 30