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2005/2006 The relative growth of information in two-dimensional partitions.
Karma Dajani, Aimee S. A. Johnson, Martijn de Vries
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Real Anal. Exchange 31(2): 397-408 (2005/2006).


Let $\overline{x} \in [0,1)^2$. In this paper we find the rate at which knowledge about the partition elements $\overline{x}$ lies in for one sequence of partitions determines the partition elements it lies in for another sequence of partitions. This rate depends on the entropy of these partitions and the geometry of their shapes, and gives a two-dimensional version of Lochs' theorem.


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Karma Dajani. Aimee S. A. Johnson. Martijn de Vries. "The relative growth of information in two-dimensional partitions.." Real Anal. Exchange 31 (2) 397 - 408, 2005/2006.


Published: 2005/2006
First available in Project Euclid: 10 July 2007

zbMATH: 1107.28011
MathSciNet: MR2265782

Primary: 28D15
Secondary: 28D20

Keywords: Lochs' theorem , Shannon-McMillan-Breiman theorem

Rights: Copyright © 2005 Michigan State University Press

Vol.31 • No. 2 • 2005/2006
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