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When is $$\mathbb R$$ the union of an increasing family of null sets? (English) Zbl 1199.28003
Summary: 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 Sierpiński sets.

##### MSC:
 28A05 Classes of sets (Borel fields, $$\sigma$$-rings, etc.), measurable sets, Suslin sets, analytic sets 03E35 Consistency and independence results
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