Majorizing measure techniques are developed and applied to Banach space theory. In particular, the following is proved.
Let B 1 and B 2 be the unit balls of [Special characters omitted.] and [Special characters omitted.] , respectively, relative to the canonical basis [Special characters omitted.] . Suppose [Special characters omitted.] . Then for every [Special characters omitted.] > 0, there exist [Special characters omitted.] with cardinality [Special characters omitted.] , and constant C depending only on [Special characters omitted.] and p, such that [Special characters omitted.] , where [Special characters omitted.] is the linear span of [Special characters omitted.] .
The following is a consequence.
Consider vectors [Special characters omitted.] in the unit ball of a Banach space X, and [Special characters omitted.] If X is of type 2 and X * is uniformly convex, then, there exists a constant C depending only on [Special characters omitted.] and [Special characters omitted.] , such that for a randomly selected subset I of cardinality [Special characters omitted.] , [Special characters omitted.] for all scalar sequence [Special characters omitted.] .
This solves a problem stated in [T2].
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