Finitely additive measures on \(S^ 2\) and \(S^ 3\), invariant with respect to rotations
type: Item
instance of: scholarly article
title: Finitely additive measures on \(S^ 2\) and \(S^ 3\), invariant with respect to rotations
zbMATH Open document ID: 0576.28019
DOI: 10.1007/BF01086166
publication date: 1984-01-01T00:00:00Z
review text: A finitely additive rotationally invariant measure on the ring of all Lebesgue measurable subsets in the n-sphere \(S^ n\) is called Ruziewicz measure. [Oeuvres avec des commentaires, vol. 1, 318-322 (1967; Zbl 0163.056)] proved, that there exist a Ruziewicz measure on \(S^ 1\), which is not proportional to Lebesgue measure. \textit{G. A. Margulis} [Monatsh. Math. 90, 233-236 (1980; Zbl 0436.43002)] and \textit{D. Sullivan} [Bull. Am. Math. Soc. New Ser. 4, 121-123 (1981; Zbl 0459.28009)] proved that every Ruziewicz measure on \(S^ n\) is proportional to Lebesgue measure if \(n\geq 4\). The author proves that every Ruziewicz measure on \(S^ 2\) and \(S^ 3\) is also proportional to Lebesgue measure.
Mathematics Subject Classification ID: 28C10
zbMATH DE Number: 3920860
zbMATH Keywords: finitely additive rotationally invariant measure
zbMATH Keywords: Ruziewicz measure
author: Vladimir Drinfeld
MaRDI profile type: Publication
cites work: Automorphic forms on GL (2)
cites work: For 𝑛>3 there is only one finitely additive rotationally invariant measure on the 𝑛-sphere defined on all Lebesgue measurable subsets
full work available at URL: https://doi.org/10.1007/bf01086166
OpenAlex ID: W2037687794
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published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 3920860