Embedding Levy Families into Banach Spaces
نویسندگان
چکیده
We prove that if a metric probability space with a usual concentration property embeds into a finite dimensional Banach space X , then X has a Euclidean subspace of a proportional dimension. In particular this yields a new characterization of weak cotype 2. We also find optimal lower estimates on embeddings of metric spaces with concentration properties into l ∞, generalizing estimates of Bourgain– Lindenstrauss–Milman, Carl–Pajor and Gluskin.
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