The aim of this note is to consider different notions for the Banach–Saks property in locally solid vector lattices as an extension for the known concepts of the Banach–Saks property in Banach lattices. We investigate relations between them; in particular, we shall characterize spaces in which, these notions agree.

中文翻译：

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从局部实体矢量晶格的角度来看，Banach-Saks属性

本说明的目的是考虑局部实体矢量晶格中Banach-Saks属性的不同概念，作为对Banach晶格中Banach-Saks属性的已知概念的扩展。我们调查他们之间的关系；特别是，我们将描述这些概念在其中相符的空间。