A Hausdorff measure inequality

Ernst, Lawrence R.; Freilich, Gerald

doi:10.1090/S0002-9947-1976-0419739-8

A Hausdorff measure inequality
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by Lawrence R. Ernst and Gerald Freilich

Trans. Amer. Math. Soc. 219 (1976), 361-368

DOI: https://doi.org/10.1090/S0002-9947-1976-0419739-8

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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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