Lévy group and density measures

Abstract

We will deal with finitely additive measures on integers extending the asymptotic density. We will study their relation to the Lévy group $\mathcal{G}$ of permutations of $\mathbb{N}$. Using a new characterization of the Lévy group $\mathcal{G}$ we will prove that a finitely additive measure extends density if and only if it is $\mathcal{G}$-invariant.

Cited by in corpus (4)

• On the notions of upper and lower density
• Extreme points of the set of density measures
• A characterization of $(\mathcal{I},\mathcal{J})$-regular matrices
• Range of density measures