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On Vitali's Theorem for Groups of Motions of Euclidean Space

On Vitali's Theorem for Groups of Motions of Euclidean Space We give a characterization of all those groups of isometric transformations of a finite-dimensional Euclidean space, for which an analogue of the classical Vitali theorem Sul problema della misura dei gruppi di punti di una retta, 1905 holds true. This characterization is formulated in purely geometrical terms. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

On Vitali's Theorem for Groups of Motions of Euclidean Space

Georgian Mathematical Journal , Volume 6 (4) – Aug 1, 1999

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Publisher
de Gruyter
Copyright
© 1999 Plenum Publishing Corporation
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.1999.323
Publisher site
See Article on Publisher Site

Abstract

We give a characterization of all those groups of isometric transformations of a finite-dimensional Euclidean space, for which an analogue of the classical Vitali theorem Sul problema della misura dei gruppi di punti di una retta, 1905 holds true. This characterization is formulated in purely geometrical terms.

Journal

Georgian Mathematical Journalde Gruyter

Published: Aug 1, 1999

Keywords: Euclidean space; group of motions; invariant measure; Vitali property; weak Vitali property

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