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In mathematics, a function f of n variables

x1, ..., xn

leads to a Chisini mean M if for every vector <x1 ... 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 the weighted variants thereof.


They were introduced by Oscar Chisini, in the paper Chisini, O. "Sul concetto di media." Periodico di Matematiche 4, 106-116, 1929.

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