From weak to strong convergence in L1-spaces via K-convergence

Abstract

A generalized version of Komlos' theorem [6], combined with a useful property of denting points in the style of [17, 22], gives a new, very ecient proof of Visintin's theorem and its generalizations [24, 2, 10, 21, 7], on equivalence of weak and strong convergence in L1 -spaces under denting point conditions.