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Capacité des Ensembles Produits

Published online by Cambridge University Press:  22 January 2016

Makoto Ohtsuka
Makoto Ohtsuka*
Affiliation:
Institut de Mathématiques, Université de Nagoya
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Si X est un ensemble mesurable au sens de Lebesgue dans un espace euclidien En et Y est un ensemble mesurable au sens de Lebesgue dans un autre espace euclidien Em, alors X × Y est mesurable dans En+m= Enx Em et sa mesure est égale au produit de la mesure de X et celle de Y. Mais il n’existe pas de telle relation simple ni pour la capacité d’ordre général ni pour la mesure de Hausdorff de dimension générale. Dans le présent mémoire nous essayons d’évaluer la capacité des ensembles produits au moyen de la capacité ou de la mesure de Hausdorff des ensembles composants.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 12 , December 1957 , pp. 95 - 130
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1957

References

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