Type, cotype, and related properties
In this chapter we will see that some of the deeper properties of Rademacher sums and Gaussian sums are intimately linked with the geometry of the Banach space in which they live. In one direction, important geometric notions such as type, cotype, and K-convexity are defined through a priori assumptions on the behaviour of random sums. In the other direction, the presence of such properties often significantly improves the behaviour of random sums.
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