On type of metric spaces

Bourgain, J.; Milman, V.; Wolfson, H.

doi:10.1090/S0002-9947-1986-0819949-8

On type of metric spaces

Authors: J. Bourgain, V. Milman and H. Wolfson
Journal: Trans. Amer. Math. Soc. 294 (1986), 295-317
MSC: Primary 46B99; Secondary 46G99, 54E35, 58C99
DOI: https://doi.org/10.1090/S0002-9947-1986-0819949-8
MathSciNet review: 819949
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Abstract: Families of finite metric spaces are investigated. A notion of metric type is introduced and it is shown that for Banach spaces it is consistent with the standard notion of type. A theorem parallel to the Maurey-Pisier Theorem in Local Theory is proved. Embeddings of ${l_p}$ -cubes into the ${l_1}$ -cube (Hamming cube) are discussed.

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