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Chisini mean

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Title: Chisini mean  
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Subject: Oscar Chisini, Means, Contraharmonic mean, Mathematical analysis, Mean
Collection: Mathematical Analysis, Means
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Chisini mean

In mathematics, a function f of n variables

x1, ..., xn

leads to a Chisini mean M if for every vector 1 ... xn>, there exists a unique M such that

f(M,M, ..., M) = f(x1,x2, ..., xn).

The arithmetic, harmonic, geometric, generalised, Heronian and quadratic means are all Chisini means, as are their weighted variants.

They were introduced by Oscar Chisini in 1929.


  • Chisini, O. "Sul concetto di media." Periodico di Matematiche 4, 106–116, 1929.
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