Property $C''$, strong measure zero sets and subsets of the plane
Volume 153 / 1997
Fundamenta Mathematicae 153 (1997), 277-293
DOI: 10.4064/fm_1997_153_3_1_277_293
Abstract
Let X be a set of reals. We show that • X has property C" of Rothberger iff for all closed F ⊆ ℝ × ℝ with vertical sections $F_x$ (x ∈ X) null, $∪_{x ∈ X}F_x$ is null; • X has strong measure zero iff for all closed F ⊆ ℝ × ℝ with all vertical sections $F_x$ (x ∈ ℝ) null, $∪_{x ∈ X}F_x$ is null.
