ABSTRACT
Let us begin by discussing the boundedness of the vector-valued Rademacher series, and its relationship to the Banach space c0 of all real sequences convergent to 0..
Definition 4.1.1. The Rademacher vector sums∑n i=1 rixi, P(ri = ±1) = 1/2, (xi) ⊂ X, are said to be
almost surely bounded if
P ( sup n
∥∥∥ n∑ i=1
rixi
∥∥∥ =∞) = 0.
