Axiomatisations of the average and a further generalisation of monotonic sequences

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.