Juan Gonz\'alez-Hern\'andez, Fernando Hern\'andez-Hern\'andez, C\'esar E. Villarreal
When is $\Bbb R$ the union of an increasing family of null sets?

Abstract: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.

Keywords: Sierp\'nski set, null sets, random forcing, rational perfect set forcing, Miller forcing
AMS Subject Classification: Primary 28A05, 03E35