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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2010 | 207 | 2 | 145-160

## Borel classes of uniformizations of sets with large sections

EN

### Abstrakty

EN
We give several refinements of known theorems on Borel uniformizations of sets with "large sections". In particular, we show that a set B ⊂ [0,1] × [0,1] which belongs to $Σ⁰_{α}$, α ≥ 2, and which has all "vertical" sections of positive Lebesgue measure, has a $Π⁰_{α}$ uniformization which is the graph of a $Σ⁰_{α}$-measurable mapping. We get a similar result for sets with nonmeager sections. As a corollary we derive an improvement of Srivastava's theorem on uniformizations for Borel sets with $G_{δ}$ sections.

145-160

wydano
2010

### Twórcy

autor
• Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic