On Hausdorff and packing dimension of product spaces-Reference-Cited by-同舟云学术

On Hausdorff and packing dimension of product spaces

Published:1996-05 Issue:4 Volume:119 Page:715-727
ISSN:0305-0041
Container-title:Mathematical Proceedings of the Cambridge Philosophical Society
language:en
Short-container-title:Math. Proc. Camb. Phil. Soc.

Author:

Howroyd J. D.

Abstract

AbstractWe show that for arbitrary metric spaces X and Y the following dimension inequalities hold:

where ‘dim’ denotes Hausdorff dimension and ‘Dim’ denotes packing dimension. The main idea of the proof is to use modified constructions of the Hausdorff and packing measure to deduce appropriate inequalities for the measure of X × Y.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference15 articles.

1. [6] Howroyd J. D. . On the theory of Hausdorff measure in metric spaces. Ph.D. thesis, University College London, 1994.

2. The measure of product and cylinder sets;Besicovitch;J. London Math. Soc.,1945

3. Die Hausdorff-Dimension von kartesischen Produktmengen in metrischen Räumen;Wegmann;J. Reine Angew. Math.,1969

4. A Method for Constructing Measures Appropriate for the Study of Cartesian Products

5. [5] Howroyd J. D. . On dimension and on the existence of subsets of finite positive Hausdorff measure. Proc. London Math. Soc., to appear.

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