Open Access
2013 Packing Measures on Cartesian Products
Ondřej Zindulka
Publ. Mat. 57(2): 393-420 (2013).


Packing measures $\mathscr{P}^{g}(E)$ and Hewitt-Stromberg measures $\boldsymbol{\nu}^{g}(E)$ and their relatives are investigated. It is shown, for instance, that for any metric spaces $X$,~$Y$ and any Hausdorff functions $f$, $g$ $$ \boldsymbol{\nu}^{g}(X)\cdot\mathscr{P}^{h}(Y)\leqslant\mathscr{P}^{gh}(X\times Y). $$ The inequality for the corresponding dimensions is established and used for a solution of a problem of Hu and Taylor: If $X\subseteq\mathbb{R}^n$, then $$ \inf\{\overline{\dim}_{\mathsf{P}} X\times Y-\overline{\dim}_{\mathsf{P}} Y:Y\subseteq\mathbb{R}^n\} =\liminf_{X_n{\nearrow} X}\underline{\dim}_{\mathsf{B}} X_n. $$ Corresponding dimension inequalities for products of measures are established


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Ondřej Zindulka. "Packing Measures on Cartesian Products." Publ. Mat. 57 (2) 393 - 420, 2013.


Published: 2013
First available in Project Euclid: 12 December 2013

zbMATH: 1285.28009
MathSciNet: MR3114775

Primary: 28A78 , 28A80 , 54E35

Keywords: Cartesian product , lower packing dimension , lower packing measure , Packing dimension , Packing measure

Rights: Copyright © 2013 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.57 • No. 2 • 2013
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