 Cotype of a Banach space

A Banach space $X$ has cotype $q$, $2\le q<\infty$, if a constant $C$ independent of the number of vectors satisfies $({\sum }_j\Vert x_j{\Vert }^q{)}^{1/q}\le C(\mathbb{E}\Vert {\sum }_j{\epsilon }_j{x}_j{\Vert }^2{)}^{1/2}$ for independent symmetric Rademacher random variables. It prevents many large vectors from having a small random sum.