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Additive set functions and the theory of probability

Published online by Cambridge University Press:  24 October 2008

J. F. C. Kingman
J. F. C. Kingman
Affiliation:
University of Sussex
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Extract

This paper is a contribution to the study of set functions which, although additive, fail to be measures by not being countably additive. It is motivated by the suggestion (to be found, for instance, in (2), section 2.3) that such functions might be used instead of measures in the theory of probability, and by speculation about the effect which the adoption of such a suggestion would have on the theory of stochastic processes.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 3 , July 1967 , pp. 767 - 776
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

(1)Doob, J. L.Stochastic processes (Wiley; New York, 1953).Google Scholar
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(3)Halmos, P. R.Measure theory (van Nostrand; Princeton, 1950).CrossRefGoogle Scholar
(4)Kingman, J. F. C. and Taylor, S. J.Introduction to measure and probability (Cambridge University Press, 1966).CrossRefGoogle Scholar
(5)Yosida, K. and Hewitt, E.Finitely additive measures. Trans. American Math. Soc. 72 (1952), 46–66.CrossRefGoogle Scholar