Portugaliæ Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
MATHEMATICA
Vol. 55, No. 1, pp. 113-128 (1998)

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A New Extension of Komlós' Theorem in Infinite Dimensions. Application: Weak Compactness in $L_X^1$

Mohammed Saadoune

Département de Mathématiques, Université Ibnou Zohr,
Lot. Addakhla B.P. 28-S, Agadir - MAROC

Abstract: A new version of Komlós' theorem in infinite dimensions is presented. It gives a different approach to well-known theorems (C. Castaing [11], A. Ülger [30] and J. Diestel-W.M. Ruess-W. Schachermayer [17]).

Keywords: Bounded sequences in $L_X^1$; Biting lemma; uniform integrability; tightness; Komlós' theorem; weak compactness.

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Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.

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