Reducible means

Abstract

A n variables mean M is said to be reducible in a certain class of means N when M can be represented as a composition of a Önite number M0; : : : ; Mr of means belonging to N , being less than n the number of variables of every Mi. In this paper, a basic classiÖcation of reducible means is developed and the notions of S-reducibility, a type of analytically decidible reducibility, and of complete reducibility of a mean are isolated. Several applications of these notions are presented. In particular, a continuous and scale invariant weighting procedure deÖned on a class M2 of two variables means is extended without losing its properties to the class of reducible means in M2.