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On a class of non-causal triangle functions

  • M. S. Ying (a1)

In [2], B. Schweizer and A. Sklar proposed the problem of whether every triangle function is causal. In [1], T. B. M. McMaster solved the problem negatively by giving an example of a non-causal triangle function. In this note we provide a class of simpler non-causal triangle functions which are continuous on a dense subset of Δ+ but in general not continuous on Δ+. Since McMaster's triangle function is also not continuous on Δ+, the problem of determining whether or not every continuous triangle function is causal remains open.

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[1]McMaster, T. B. M.. A non-causal triangle function. Math. Proc. Cambridge Philos. Soc. 101 (1987), 287290.
[2]Schweizer, B. and Sklar, A.. Probabilistic Metric Spaces (North-Holland, 1983).
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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