Geodesic
Property $C''$, strong measure zero sets and subsets of the plane
Fundamenta Mathematicae, Tome 153 (1997) no. 3, pp. 277-293.

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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.
DOI : 10.4064/fm_1997_153_3_1_277_293

Janusz Pawlikowski 1

1 
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Janusz Pawlikowski. Property $C''$, strong measure zero sets and subsets of the plane. Fundamenta Mathematicae, Tome 153 (1997) no. 3, pp. 277-293. doi : 10.4064/fm_1997_153_3_1_277_293. http://geodesic.mathdoc.fr/articles/10.4064/fm_1997_153_3_1_277_293/

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