Geodesic
Axiomatisations of the average and a further generalisation of monotonic sequences
Glasgow mathematical journal, Tome 15 (1974) no. 1, pp. 63-65

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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. 
Bibby, John. Axiomatisations of the average and a further generalisation of monotonic sequences. Glasgow mathematical journal, Tome 15 (1974) no. 1, pp. 63-65. doi: 10.1017/S0017089500002135
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[1] 1.Copson, E. T., On a generalisation of monotonic sequences, Proc. Edinburgh Math. Soc. 17 (1970), 159–164. Google Scholar | DOI

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