On the complexity of sums of Dirichlet measures
type: Item
instance of: scholarly article
title: On the complexity of sums of Dirichlet measures
zbMATH Open document ID: 0766.28001
author: Sylvain Kahane
publication date: 1993-06-13T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74983
review text: Let \(M\) be the set of all Dirichlet measures on the unit circle. We prove that \(M+M\) is a non Borel analytic set for the weak* topology and that \(M+M\) is not norm-closed. More precisely, we prove that there is no weak* Borel set which separates \(M+M\) from \(D^ \perp\) (or even \(L^ \perp_ 0)\), the set of all measures singular with respect to every measure in \(M\). This extends results of Kaufman, Kechris and Lyons about \(D^ \perp\) and \(H^ \perp\) and gives many examples of non Borel analytic sets.
Mathematics Subject Classification ID: 28A33
Mathematics Subject Classification ID: 28A05
Mathematics Subject Classification ID: 28A12
Mathematics Subject Classification ID: 03E15
zbMATH DE Number: 179550
zbMATH Keywords: singular measures
zbMATH Keywords: Dirichlet measures on the unit circle
zbMATH Keywords: non Borel analytic set
zbMATH Keywords: weak* Borel set
MaRDI profile type: Publication
OpenAlex ID: W2321082495
cites work: Antistable classes of thin sets in harmonic analysis
cites work: Topics on analytic sets
cites work: Ordinal Rankings on Measures Annihilating Thin Sets
cites work: Mixing and asymptotic distribution modulo 1
DOI: 10.5802/AIF.1323
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published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 179550