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arXiv · 2004.12578

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

Yerlan Nessipbayev·Kanat Tulenov
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Abstract

In this paper, we provide a direct proof for the equivalence of K.M. Chong's and De la Vall\'{e}e 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 $L_1(0, \infty)$.

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Yerlan Nessipbayev, Kanat Tulenov. 2020-04-27. Weak compactness criteria in $L_1$ space in terms of Orlicz function. https://arxiv.org/abs/2004.12578

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