On the distribution of Sidon series

  title={On the distribution of Sidon series},
  author={Nakhl{\'e} Habib Asmar and Stephen Montgomery-Smith},
Let B denote an arbitrary Banach space, G a compact abelian group with Haar measure μ and dual group Γ. Let E be a Sidon subset of Γ with Sidon constant S(E). Let rn denote the n-th Rademacher function on [0, 1]. We show that there is a constant c, depending only on S(E), such that, for all α > 0: c−1P ∥∥∥∥ N ∑ n=1 anrn ∥∥∥∥ ≥ cα ] ≤ μ ∥∥∥∥ N ∑ 

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