Existence of an invariant measure on a topological quasigroup
type: Item
instance of: scholarly article
title: Existence of an invariant measure on a topological quasigroup
zbMATH Open document ID: 1439.54021
published in: Topology and its Applications
publication date: 2020-04-07T00:00:00Z
review text: Let \(G\) be a unital quasigroup, i.e. a set with a multiplication \(G^2\ni (a,b)\mapsto ab\in G\) and a neutral element such that for any \(a,b\in G\) both the equations \(ax=b\) and \(ya=b\) have a unique solution. Assume that \(G\) is endowed with a Tychonoff topology such that the multiplication, the right division and the left division are jointly continuous. The main theorem says: If \(G\) admits a nontrivial left invariant \([0,+\infty]\)-valued \(\sigma\)-additive Borel measure \(\mu\) such that the family of all bounded uniformly continuous functions of \(L^2(G,\mu,\mathbb{C})\) is dense in \(L^2(G,\mu,\mathbb{C})\), then \(G\) is a dense unital subquasigroup of a locally compact unital quasigroup.
reviewed by: Hans Weber
Mathematics Subject Classification ID: 54H11
Mathematics Subject Classification ID: 54D45
Mathematics Subject Classification ID: 43A05
Mathematics Subject Classification ID: 28C10
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 22A30
zbMATH DE Number: 7187687
zbMATH Keywords: topological quasigroup
zbMATH Keywords: measure
zbMATH Keywords: left invariant
zbMATH Keywords: locally compact
author: Sergey V. Ludkovsky
MaRDI profile type: Publication
full work available at URL: j.topol.2020.107147
OpenAlex ID: W3010395599
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DOI: 10.1016/J.TOPOL.2020.107147
description: scientific article; zbMATH DE number 7187687