Title

The Relative Growth On Information In Two-Dimensional Partitions

Document Type

Article

Publication Date

2005

Published In

Real Analysis Exchange

Abstract

Let ... ∈ [0, 1)^sup 2^. In this paper we find the rate at which knowledge about the partition elements ... 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.