ON A THEOREM OF KWAPIEŃ

Abstract

If (Ω, Σ, v) is the Cantor group with its resident Haar measure, X a Banach space and {x_n} a sequence in X, a classic thorem of Kwapień is used in this note to investigate the relationship between the convergence of the series Σ ^∞,n=1 w_nn_n in L₁ (v, X) and the the existence of certain convergent subseries of Σ ^∞, n=1 x_n in X.