Axiomatic Characterization of the Mean Function on Trees

A mean of a sequence π = (x 1 , x 2 , …, x k ) of elements of a finite metric space (X, d) is an element x for which [Formula: see text] is minimum. The function Mean whose domain is the set of all finite sequences on X and is defined by Mean (π) = {x|x is a mean of π} is called the mean function on X. In this note, the mean function on finite trees is characterized axiomatically.