This article is cited in 2 papers

Entropy Extension

A. E. Litvak^a, V. D. Milman^b, A. Pajor^c, N. Tomczak-Jaegermann<sup>a

a</sup> University of Alberta
^b Tel Aviv University, School of Mathematical Sciences
^c Université de Marne-la-Vallée

Abstract: We prove an “entropy extension-lifting theorem.” It consists of two inequalities for the covering numbers of two symmetric convex bodies. The first inequality, which can be called an “entropy extension theorem,” provides estimates in terms of entropy of sections and should be compared with the extension property of $\ell_{\infty}$. The second one, which can be called an “entropy lifting theorem,” provides estimates in terms of entropies of projections.

Keywords: metric entropy, entropy extension, entropy lifting, entropy decomposition, covering numbers.

UDC: 517.9

Received: 18.05.2006

DOI: 10.4213/faa853

 English version: Functional Analysis and Its Applications, 2006, 40:4, 298–303

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