Measures on circle coarse-grained systems of sets
type: Item
instance of: scholarly article
title: Measures on circle coarse-grained systems of sets
zbMATH Open document ID: 1196.28003
author: Anna De Simone
author: Pavel Pták
published in: Positivity
publication date: 2010-08-13T00:00:00Z
review text: Let \(\mathcal{C}\) be the unit circle parametrized within \([0,2\pi[\), \(n\in\mathbb{N}\) and \(\Delta_n\) the quantum logic generated by the intervals \([a,a+\frac{2\pi}{n}[\), \(a\in [0,2\pi[\), i.e. the smallest system of subsets of \(\mathcal{C}\) which contains these intervals and is closed under the formation of disjoint unions and complements in \(\mathcal{C}\). The main theorem says that any finitely additive probability measure \(m:\Delta_n\rightarrow [0,1]\) can be extended to a measure over the Boolean algebra of all subsets of \(\mathcal{C}\). As observed by the authors standard techniques cannot be used for the proof since \(\Delta_n\) is not closed under intersections.
reviewed by: Hans Weber
Mathematics Subject Classification ID: 28A12
Mathematics Subject Classification ID: 28E99
Mathematics Subject Classification ID: 06C15
zbMATH DE Number: 5770260
zbMATH Keywords: finitely additive measure
zbMATH Keywords: measure extension
zbMATH Keywords: quantum logic
MaRDI profile type: Publication
full work available at URL: s11117-009-0015-6
OpenAlex ID: W2033753235
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DOI: 10.1007/S11117-009-0015-6
description: scientific article; zbMATH DE number 5770260