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Funktsional'nyi Analiz i ego Prilozheniya, 2006, Volume 40, Issue 4, Pages 65–71
DOI: https://doi.org/10.4213/faa853 (Mi faa853) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Entropy Extension

A. E. Litvaka, V. D. Milmanb, A. Pajorc, N. Tomczak-Jaegermanna

a University of Alberta
b Tel Aviv University, School of Mathematical Sciences
c Université de Marne-la-Vallée
Full-text PDF (166 kB) Citations (2)
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DOI: https://doi.org/10.4213/faa853
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.
Received: 18.05.2006
English version:
Functional Analysis and Its Applications, 2006, Volume 40, Issue 4, Pages 298–303
DOI: https://doi.org/10.1007/s10688-006-0046-8
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: A. E. Litvak, V. D. Milman, A. Pajor, N. Tomczak-Jaegermann, “Entropy Extension”, Funktsional. Anal. i Prilozhen., 40:4 (2006), 65–71; Funct. Anal. Appl., 40:4 (2006), 298–303
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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