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On a class of non-causal triangle functions

Published online by Cambridge University Press:  24 October 2008

M. S. Ying
Affiliation:
Department of Mathematics, Fuzhou Teacher's College, Jiangxi, China

Extract

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.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

REFERENCES

[1]McMaster, T. B. M.. A non-causal triangle function. Math. Proc. Cambridge Philos. Soc. 101 (1987), 287290.CrossRefGoogle Scholar
[2]Schweizer, B. and Sklar, A.. Probabilistic Metric Spaces (North-Holland, 1983).Google Scholar

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