Any interior point of a finite interval on the real line canbe interpreted as dual Fréchet means

Author

Nielsen, Frank

Abstract

In this note, we show that any interior point of an open interval on the real line can be interpreted as a pair of dual Fréchet quasi-arithmetic means associated with dual metric distances. A Riemannian interpretation of the Euclidean line brings to light a novel concept of dual scales of means, grounded in convex duality and of independent interest.