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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A Hausdorff measure inequality


Authors: Lawrence R. Ernst and Gerald Freilich
Journal: Trans. Amer. Math. Soc. 219 (1976), 361-368
MSC: Primary 28A75
MathSciNet review: 0419739
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Abstract: We prove that the Hausdorff $ (m + k)$-measure of a product set is no less than the product of the Hausdorff m-measure of the (measurable) first component set in $ {{\mathbf{R}}^m}$ and the (finite) Hausdorff k-measure of the second component in $ {{\mathbf{R}}^n}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0419739-8
PII: S 0002-9947(1976)0419739-8
Keywords: Hausdorff measure, product set
Article copyright: © Copyright 1976 American Mathematical Society