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1998/1999 Sets with Different Dimensions in [0, 1]
Donald W. Spear
Real Anal. Exchange 24(1): 373-390 (1998/1999).

Abstract

Given $0 < s < u < v < 1$ and $s < t < v$, a Cantor set $Y$ is constructed in $[0, 1]$ with Hausdorff dimension $s$, packing dimension $t$, lower box dimension $u$ and upper box dimension $v$. In the sense that $t$ and $u$ are independent, so are the packing and lower box dimensions. Although $Y = \{0\} \cup \bigcup_{ \ell=0}^{ \infty} Y_\ell$, the lower and upper box dimensions of each $Y_\ell$ are respectively $s$ and $t$.

Citation

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Donald W. Spear. "Sets with Different Dimensions in [0, 1]." Real Anal. Exchange 24 (1) 373 - 390, 1998/1999.

Information

Published: 1998/1999
First available in Project Euclid: 23 March 2011

zbMATH: 0940.28008
MathSciNet: MR1691757

Subjects:
Primary: 28A75, 28A78

Keywords: dimension

Rights: Copyright © 1998 Michigan State University Press

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