Abstract
We prove the uniform concentration of Lebesgue measure phenomenon on the ball of ℓ n p for 1 ≤ p ≤ 2. In particular, we give a first concentration inequality for Lebesgue measure on the ball of ℓ n1 . An application is the lower exponential bound on the dimension of ℓ∞ admitting an isomorphic embedding of ℓ n1 and on the distortion of such those embeddings, proved in [L].
Research supported by DGICYT grant #PB96-1327. This paper includes part of the Ph.D. thesis of the second author.
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Arias-de-Reyna, J., Villa, R. (2000). The uniform concentration of measure phenomenon in ℓ n p (1 ≤ p ≤ 2). In: Milman, V.D., Schechtman, G. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1745. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0107203
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DOI: https://doi.org/10.1007/BFb0107203
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