Abstract
In this paper, starting with the work of Kolmogorov on continuous means, we define the four properties, Symmetry, Internality, Monotonicity, and Associativity that a discrete mean should satisfy. An extremal mean is then a (discrete) mean whose output depends only on the maximum and minimum of the input set. We prove that any integer mean must be extremal.
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Virtue is the Mean Between Two Extremes (Aristotle: Nicomachean Ethics, Book II).
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Bennett, C.D., Holland, W.C. & Székely, G.J. Integer valued means. Aequat. Math. 88, 137–149 (2014). https://doi.org/10.1007/s00010-013-0217-7
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DOI: https://doi.org/10.1007/s00010-013-0217-7