On an axiomatization of the quasi-arithmetic mean values without the symmetry axiom | Zendy

JeanLuc Marichal | Zendy

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On an axiomatization of the quasi-arithmetic mean values without the symmetry axiom

Author(s) -

JeanLuc Marichal

Publication year - 2000

Publication title -

aequationes mathematicae

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.564

H-Index - 35

eISSN - 1420-8903

pISSN - 0001-9054

DOI - 10.1007/pl00000129

Subject(s) - mathematics , axiom of choice , axiom , axiom independence , symmetry (geometry) , zermelo–fraenkel set theory , pure mathematics , algebra over a field , arithmetic , set theory , geometry , set (abstract data type) , computer science , programming language

Summary. Kolmogoroff and Nagumo proved that the quasi-arithmetic means correspond exactly to the decomposable sequences of continuous, symmetric, strictly increasing in each variable and reflexive functions. We replace decomposability and symmetry in this characterization by a generalization of the decomposability.

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