Strongly meager sets and subsets of the plane

Pawlikowski, Janusz

Fundamenta Mathematicae, Tome 158 (1998), p. 279-287 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $X \subseteq 2^{w}$ . Consider the class of all Borel $F \subseteq X \times 2^{w}$ with null vertical sections $F_{x}$ , x ∈ X. We show that if for all such F and all null Z ⊆ X, $\cup_{x \in Z} F_{x}$ is null, then for all such F, $\cup_{x \in X} F_{x} \neq 2^{w}$ . The theorem generalizes the fact that every Sierpiński set is strongly meager and was announced in [P].

Publié le : 1998-01-01

Zbl 0906.04001

EUDML-ID : urn:eudml:doc:212273

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     author = {Janusz Pawlikowski},
     title = {Strongly meager sets and subsets of the plane},
     journal = {Fundamenta Mathematicae},
     volume = {158},
     year = {1998},
     pages = {279-287},
     zbl = {0906.04001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv156i3p279bwm}
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Pawlikowski, Janusz. Strongly meager sets and subsets of the plane. Fundamenta Mathematicae, Tome 158 (1998) pp. 279-287. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv156i3p279bwm/

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