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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2009 | 205 | 2 | 105-115

## Can we assign the Borel hulls in a monotone way?

EN

### Abstrakty

EN
A hull of A ⊆ [0,1] is a set H containing A such that λ*(H) = λ*(A). We investigate all four versions of the following problem. Does there exist a monotone (with respect to inclusion) map that assigns a Borel/$G_{δ}$ hull to every negligible/measurable subset of [0,1]?
Three versions turn out to be independent of ZFC, while in the fourth case we only prove that the nonexistence of a monotone $G_{δ}$ hull operation for all measurable sets is consistent. It remains open whether existence here is also consistent. We also answer the question of Z. Gyenes and D. Pálvölgyi whether monotone hulls can be defined for every chain of measurable sets. Moreover, we comment on the problem of hulls of all subsets of [0,1].

105-115

wydano
2009

### Twórcy

autor
• Rényi Alfréd Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary
autor
• Eötvös Loránd University, Department of Analysis, Pázmány Péter sétány 1/c, H-1117 Budapest, Hungary