Abstract
This note consists of two parts. In the first part, we give a new proof of Urysohn's inequality relating a volume ratio of a central symmetric convex body K and the euclidean ball to the integral average E K *. We use this inequality in the second part through entropy estimations to give a new and very simple proof of the result from [BM1] that the volume ratios of the cotype 2-spaces are uniformly bounded by a constant depending only on the cotype 2-constant of a space.
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© 1987 Springer-Verlag
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Milman, V.D. (1987). Some remarks on Urysohn's inequality and volume ratio of cotype 2-spaces. In: Lindenstrauss, J., Milman, V.D. (eds) Geometrical Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078137
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DOI: https://doi.org/10.1007/BFb0078137
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