Abstract
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.
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