Let $\left( X _ { i } \right) _ { i \in \mathbf { N } }$ be a sequence of independent random variables all following a Rademacher distribution. Let the map $\psi : u \in \mathbf { R } ^ { ( \mathbf { N } ) } \mapsto \sum _ { i = 0 } ^ { + \infty } u _ { i } X _ { i }$. We denote $R = \psi \left( \mathbf { R } ^ { ( \mathbf { N } ) } \right)$. Show that for all $p , q \in \left[ 1 , + \infty \right[$, the norms $\| \cdot \| _ { p }$ and $\| \cdot \| _ { q }$ are equivalent on $R$.