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Axiomatisations of the average and a further generalisation of monotonic sequences

Published online by Cambridge University Press:  18 May 2009

John Bibby
John Bibby
Affiliation:
Department of Statistics, University of St. Andrews
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A bounded monotonic sequence is convergent. This paper shows that a bounded sequence which is g-monotonic (to be defined) also converges. The proof generalises one attributed to Professor R. A. Rankin by Copson [1]. The theorem requires two definitions: the first axiomatises the notion of “average“ and the second generalises the concept of monotonicity.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 15 , Issue 1 , March 1974 , pp. 63 - 65
Copyright
Copyright © Glasgow Mathematical Journal Trust 1974

References

REFERENCE

1.Copson, E. T., On a generalisation of monotonic sequences, Proc. Edinburgh Math. Soc. 17 (1970), 159–164.CrossRefGoogle Scholar