The Journal of Analysis

, Volume 27, Issue 4, pp 943–984 | Cite as

Reducible means

  • Lucio R. BerroneEmail author
Original Research Paper


A n variables mean M is said to be reducible in a certain class of means \(\mathcal {N}\) when M can be represented as a composition of a finite number \(M_{0},\ldots ,M_{r}\) of means belonging to \(\mathcal {N}\), being less than n the number of variables of every \(M_{i}\). In this paper, a basic classification 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 defined on a class \(\mathcal {M}_{2}\) of two variables means is extended without losing its properties to the class of reducible means in \(\mathcal {M}_{2}\).


Means Clones Representation Reducibility 

Mathematics Subject Classification

26E60 08A75 20M30 26D07 



The author expresses his appreciation to the anonymous Referee whose criticism helped to improve the quality of this paper.

Compliance with ethical standards

Conflict of interest

The author declares that he has no conflict of interest.


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Copyright information

© Forum D'Analystes, Chennai 2018

Authors and Affiliations

  1. 1.Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Laboratorio de Acústica y Electroacústica, Facultad de Cs. Exactas, Ing. y Agrim.Univ. Nac. de RosarioRosarioArgentina

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