Means on equivalence relations
type: Item
instance of: scholarly article
title: Means on equivalence relations
zbMATH Open document ID: 1140.37003
author: Alexander S. Kechris
author: Benjamin D. Miller
published in: Israel Journal of Mathematics
publication date: 2008-05-27T00:00:00Z
review text: A mean on a countable set \(A\) is a positive linear functional \(\phi:\ell^{\infty}(A)\to\mathbb C\) sending the constant sequence \((1)\) to \(1\). An assignment of means on a countable Borel equivalence relation \(E\) on a Polish space \(X\) is a map that associates a mean on each equivalence class to each equivalence class. The equivalence relation is called smooth if there is a Borel section for it (that is, a Borel subset that contains exactly one representative of each class). The main result here is that \(E\) admits a Borel assignment of means if and only if \(E\) is smooth. This is derived as a consequence of a more technical characterization of the existence of a Baire assignment of means.
Mathematics Subject Classification ID: 37A20
Mathematics Subject Classification ID: 28D15
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 37A15
zbMATH DE Number: 5279160
zbMATH Keywords: Borel set
zbMATH Keywords: smooth equivalence relation
Wikidata QID: Q56989947
reviewed by: Thomas B. Ward
MaRDI profile type: Publication
full work available at URL: s11856-008-0011-8
OpenAlex ID: W1972195264
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DOI: 10.1007/S11856-008-0011-8
description: scientific article; zbMATH DE number 5279160