We introduce the notions of λ-Baire property and λ-semiopen set using sets of Lebesgue measure zero. For a family A of subsets of the real line, we define the (λ^∗)-property analogously as it was done in the category case for the (∗)-property. The main result is that the family A of all subsets of the real line having the λ-Baire property has the (λ^∗)-property iff A is situated between the Euclidean topology and the family of λ-semiopen sets.

中文翻译：

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连续性和测度

我们使用Lebesgue度量零集介绍了λ- Baire属性和λ-半开放集的概念。对于实线子集的族A，我们定义（λ ^∗）属性的方式类似于在（∗）属性的类别情况下所做的。主要结果是，具有λ- Baire属性的实线所有子集的族A具有（λ ^∗）属性，当iff A位于欧几里得拓扑和λ-半开放集族之间时。