Entropy numbers and covering numbers of sets and operators are well known geometric notions, which found many applications in various fields of mathematics, statistics, and computer science. Their values for finite-dimensional embeddings $id:{\ell }_p^n\to {\ell }_q^n$, $0<p,q\le \infty$, are known (up to multiplicative constants) since the pioneering work of Schütt in 1984, with later improvements by Edmunds and Triebel, Kühn and Guédon and Litvak. The aim of this survey is to give a self-contained presentation of the result and an overview of the different techniques used in its proof.

中文翻译：

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有限维嵌入的熵数

熵数以及集合和运算符的覆盖数是众所周知的几何概念，在数学，统计学和计算机科学的各个领域中都有许多应用。它们对于有限维嵌入的值$\mathrm{一世}d：{\ell }_p^{ñ}\to {\ell }_q^{ñ}$， $0<p，q\le \infty$自从1984年Schütt的开创性工作以来，已知，，（直到乘法常数），后来由Edmunds和Triebel，Kühn，Guédon和Litvak进行了改进。这项调查的目的是对结果进行独立的介绍，并概述其证明中使用的不同技术。