Chisini mean

In mathematics, a function f of n variables

x₁, ..., x_n

leads to a Chisini mean M if for every vector <x₁ ... x_n>, there exists a unique M such that

f(M,M, ..., M) = f(x₁,x₂, ..., x_n).

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.

References

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

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