Original Articles

ON A THEOREM OF KWAPIEŃ

Published in: Quaestiones Mathematicae
Volume 24 , issue 1 , 2001 , pages: 51–54

DOI: 10.1080/16073606.2001.9639772

Author(s): J.C. Ferrando Departamento de Estadística y Matemática Aplicada, Spain

Keywords: 46B15 , 46B09 , 46B15 , 46B09

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.

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