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.

References

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

Categories:

Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать курсовую

Mean — This article is about the statistical concept. For other uses, see Mean (disambiguation). In statistics, mean has two related meanings: the arithmetic mean (and is distinguished from the geometric mean or harmonic mean). the expected value of a… … Wikipedia
Oscar Chisini — (March 4, 1889 – April 10, 1967) was an Italian mathematician. He introduced the Chisini mean in 1929. Biography Chisini was born in Bergamo. In 1929 he founded the Institute of Mathematics (Istituto di Matematica) at the University of Mil … Wikipedia
List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… … Wikipedia
Canonical bundle — In mathematics, the canonical bundle of a non singular algebraic variety V of dimension n is the line bundle which is the nth exterior power of the cotangent bundle Ω on V. Over the complex numbers, it is the determinant bundle of holomorphic n… … Wikipedia