Inequalities for entropies and dimensions
Alexander Shen
TL;DR
This paper reveals a geometric interpretation of entropy inequalities through Hausdorff and packing dimensions, connecting information theory with geometric measure theory using the point-to-set principle.
Contribution
It introduces a novel geometric perspective on entropy inequalities by linking them to dimensions and known complexity results.
Findings
Linear entropy inequalities correspond to geometric dimension inequalities.
The point-to-set principle bridges entropy and geometric dimensions.
Results unify information theory with geometric measure theory.
Abstract
We show that linear inequalities for entropies have a natural geometric interpretation in terms of Hausdorff and packing dimensions, using the point-to-set principle and known results about inequalities for complexities, entropies and the sizes of subgroups.
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Taxonomy
TopicsAnalytic and geometric function theory · Mathematical Dynamics and Fractals · Advanced Topology and Set Theory