关键词: weak Orlicz space,   convergence theorem, conditional compactness

Abstract:

In this article, a class of weak Orlicz function spaces is defined and their basic properties are discused. In particular, for the sequences in weak Orlicz space, we establish several basic convergence theorems including bounded convergence theorem, control convergence theorem and Vitali-type convergence theorem and so on. Moreover, the conditional compactness of its subsets is also discussed.

Key words: weak Orlicz space,   convergence theorem, conditional compactness