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arXiv · 2507.03338

Local entropy theory, combinatorics, and local theory of Banach spaces

Hanfeng Li·Kairan Liu
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Abstract

Each continuous action of a countably infinite discrete group $\Gamma$ on a compact metrizable space X induces a continuous action of $\Gamma$ on the space M(X) of Borel probability measures on X. We compare the local entropy theory for these two actions, and describe the relation between their IE-tuples. Several other types of tuples are also studied. Our main tool is a new combinatorial lemma. We also give an application of the combinatorial lemma to the local theory of Banach spaces.

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Hanfeng Li, Kairan Liu. 2025-07-04. Local entropy theory, combinatorics, and local theory of Banach spaces. https://arxiv.org/abs/2507.03338

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