A Hausdorff measure inequality

Author:

Ernst Lawrence R.,Freilich Gerald

Abstract

We prove that the Hausdorff ( m + k ) (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 R m {{\mathbf {R}}^m} and the (finite) Hausdorff k-measure of the second component in R n {{\mathbf {R}}^n} .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference5 articles.

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2. A proof that \cal𝐻² and \cal𝑇² are distinct measures;Ernst, Lawrence R.;Trans. Amer. Math. Soc.,1974

3. Die Grundlehren der mathematischen Wissenschaften, Band 153;Federer, Herbert,1969

4. On the measure of Cartesian product sets;Freilich, Gerald;Trans. Amer. Math. Soc.,1950

5. Convexly generated 𝑘-dimensional measures;Moore, Edward F.;Proc. Amer. Math. Soc.,1951

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1. Boundary regularity for the supercritical Lane-Emden heat flow;Calculus of Variations and Partial Differential Equations;2015-06-07

2. Multifractal dimensions of product measures;Mathematical Proceedings of the Cambridge Philosophical Society;1996-11

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