Geodesic
Entropy Extension
Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 4, pp. 65-71

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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. 
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     author = {A. E. Litvak and V. D. Milman and A. Pajor and N. Tomczak-Jaegermann},
     title = {Entropy {Extension}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2006_40_4_a5/}
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A. E. Litvak; V. D. Milman; A. Pajor; N. Tomczak-Jaegermann. Entropy Extension. Funkcionalʹnyj analiz i ego priloženiâ, Tome 40 (2006) no. 4, pp. 65-71. http://geodesic.mathdoc.fr/item/FAA_2006_40_4_a5/