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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.
Georgian Mathematical Journal – de Gruyter
Published: Aug 1, 1999
Keywords: Euclidean space; group of motions; invariant measure; Vitali property; weak Vitali property
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