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- W2068460345 abstract "A la suite des travaux de Lebesgue, Hausdorff a prouvé la non-existence d'une mesure positive, non nulle, invariante, dénombrablement additive sur toutes les parties bornées de Rn(n ≥ 1); il n'existe pas de mesure positive, non nulle, invariante, ayant la propriété de l'additivité finie sur Rn(n ≥ 3). Par contre, Banach a produit des mesures de ce dernier type dans les cas n = 1, 2. L'interprétation du phénomène a été donnée par von Neumann dans le cadre des groupes moyennables. Ruziewicz a soulevé le problème de l'unicité de l'intégrale de Lebesgue. After Lebesgue's measure had been defined, Hausdorff showed the nonexistence of positive, nontrivial, invariant, completely additive measures over all subsets of Rn(n ≥ 1); there does not exist a positive, nontrivial, invariant, finitely additive measure on Rn(n ≥ 3) either. Banach produced a measure of the latter type for the cases n = 1, 2. Von Neumann furnished an interpretation of the phenomenon in the framework of amenable groups. Ruziewicz raised the problem of the uniqueness of Lebesgue's measure. Nachdem das Lebesguesche Maß definiert worden war, zeigte Hausdorff, daß kein positives, nicht triviales, invariantes Maß auf allen Teilen von Rn(n ≥ 1) besteht, das vollständig additiv ist; es gibt auch kein positives, nicht triviales, invariantes, endlich additives Maß für Rn(n ≥ 3). Banach gab ein Maß vom zweiten Typus für die Fälle n = 1, 2 an. Von Neumann erläuterte das Phänomen im Rahmen der mittelbaren Gruppen. Ruziewicz stellte die Frage nach der Eindeutigkeit des Lebesgueschen Maßes." @default.
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- W2068460345 date "1986-08-01" @default.
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- W2068460345 title "Mesures invariantes—De Lebesgue à nos jours" @default.
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