Quasiarithmetic-type invariant means on probability space

Abstract

For a family $({\mathcal{A}}_x{)}_{x\in (0,1)}$ of integral quasiarithmetic means sattisfying certain measurability-type assumptions we search for an integral mean $K$ such that $K(({\mathcal{A}}_x(\mathbb{P}){)}_{x\in (0,1)})=K(\mathbb{P})$ for every compactly supported probabilistic Borel measure $\mathbb{P}$. Also some results concerning the uniqueness of invariant means will be given.

References in corpus (7)

• Computer aided solution of the invariance equation for two-variable Gini means
• Computer aided solution of the invariance equation for two-variable Stolarsky means
• Characterization of generalized quasi-arithmetic means
• Invariant means and iterates of mean-type mappings
• Limit properties in a family of quasi-arithmetic means
• Invariant property for discontinuous mean-type mappings
• On the quasi-arithmetic Gauss-type iteration

Cited by in corpus (1)

• Invariance property for extended means