Weak compactness criteria in $L_1$ space in terms of Orlicz function

Abstract

In this paper, we provide a direct proof for the equivalence of K.M. Chong's and De la Vallée Poussin's criteria of weak compactness of a subset $K$ of $L_1(0,1)$ in terms of some Orlicz function. Furthermore, we discuss the equivalence in $L_1(0,\infty )$.

10