Geodesic
When is $\Bbb R$ the union of an increasing family of null sets?
Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 4, pp. 623-630.

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We study the problem in the title and show that it is equivalent to the fact that every set of reals is an increasing union of measurable sets. We also show the relationship of it with Sierpi'nski sets.
Classification : 03E35, 28A05
Keywords: Sierp'nski set; null sets; random forcing; rational perfect set forcing; Miller forcing 
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González-Hernández, Juan; Hernández-Hernández, Fernando; Villarreal, César E. When is $\Bbb R$ the union of an increasing family of null sets?. Commentationes Mathematicae Universitatis Carolinae, Tome 48 (2007) no. 4, pp. 623-630. http://geodesic.mathdoc.fr/item/CMUC_2007__48_4_a5/