Real Analysis Exchange

The relative growth of information in two-dimensional partitions.

Karma Dajani, Aimee S. A. Johnson, and Martijn de Vries

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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.

Article information

Real Anal. Exchange Volume 31, Number 2 (2005), 397-408.

First available in Project Euclid: 10 July 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 28D15: General groups of measure-preserving transformations
Secondary: 28D20: Entropy and other invariants

Lochs' theorem Shannon-McMillan-Breiman Theorem


Dajani, Karma; de Vries, Martijn; Johnson, Aimee S. A. The relative growth of information in two-dimensional partitions. Real Anal. Exchange 31 (2005), no. 2, 397--408.

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