Strongly meager sets and subsets of the plane
Volume 156 / 1998
Fundamenta Mathematicae 156 (1998), 279-287
DOI: 10.4064/fm-156-3-279-287
Abstract
Let $X ⊆ 2^w$. Consider the class of all Borel $F ⊆ X×2^w$ with null vertical sections $F_x$, x ∈ X. We show that if for all such F and all null Z ⊆ X, $∪_{x ∈ Z}F_x$ is null, then for all such F, $∪_{x ∈ X}F_x≠2^w$. The theorem generalizes the fact that every Sierpiński set is strongly meager and was announced in [P].
