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.

See also

• Fréchet mean
• Generalized mean
• Jensen's inequality
• Quasi-arithmetic mean
• Stolarsky mean

References

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