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An Isoperimetric Theorem on the Cube and the Kintchine-Kahane Inequalities
For vectors ${x_1}, \ldots , {x_n}$ in a Banach space, we bound the deviation of $\left \| {\sum \nolimits _{i \leq n} {{\varepsilon _i}{x_i}} } \right \|$ from its median.